Put-call futures parity and liquidity provision by trader ......data, we divide traders by types...

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Liquidity providing in arbitrage by trader types: Evidence from the

Taiwan index option market

Chin-Ho Chena, Junmao Chiub, Huimin Chungc

a Postdoctoral scholar, Graduate Institute of Finance, National Chiao Tung University, 1001 Ta-Hsueh Road,

Hsinchu 30050, Taiwan b Assistant Professor, College of Management, Yuan Ze University, 135 Yuan-Tung Road, Chung-Li, Taoyuan

32003, Taiwan c Professor, Graduate Institute of Finance, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu 30050,

Taiwan

This version: January 2015

___________________________________________________________________________

Abstract

Arbitraging in put-call futures parity (PCFP) violations may impair liquidity due to created

adverse select costs and order imbalances. This study explores the liquidity providing in the

period of arbitrage exploitation by trader types. Using the unique dataset of the Taiwan index

option (TXO) with identified trade types, our results provide evidence that individual traders

play a much more dominant role in driving option prices to violate the PCFP. In terms of

arbitrage shocks, market makers dominate the response of liquidity supply while individual

and domestic institutional traders respond less. Our results support that market markers do their

formal market making obligation as the TXO market demand unexpected liquidity. Besides,

the impact of submitted limit orders on liquidity of option is different during times of before

and after violating PCFP. An increase in submitted limit orders enhances liquidity during times

of before violating PCFP but deteriorates liquidity during times of after violating PCFP.

Keywords: Put call futures parity, Trader type, Liquidity provision, Index option market, Adverse selection

JEL Classification: G10; G11; G14

Corresponding author: Tel: +886-3-5712121, ext. 57075; Fax: +886-3-5733260. E-mail addresses: chinho.

[email protected] (C.H. Chen), [email protected] (J. Chiu), [email protected] (H. Chung).

mailto:chinho.%[email protected]

mailto:chinho.%[email protected]

mailto:[email protected]

mailto:[email protected]

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1. Introduction

Arbitrage is fundamental to and important for financial markets. Despite arbitrage stimulates

market price efficiency by enforcing the Law of One Price (LOP), it can also deteriorate

liquidity. Recent studies show that arbitrage worsens, rather than enhances, liquidity if

arbitrage creates adverse selection costs (Domowitz, Glen, & Madhavan, 1998; Kumar & Seppi,

1994; Foucault, Kozhan, & Tham, 2014).1 For example, Foucault et al. (2014) document that

asynchronous price adjustments in asset pairs following new information arrival can cause

toxic arbitrage opportunities due to created adverse selection costs for liquidity providers. This

is because as enforcing these toxic opportunities, arbitrageurs expose the liquidity providers to

the risk of trading at stale quotes, i.e., being picked off. As a result, the liquidity providers with

stale quotes will incur a loss on the trade as if they have been trading with better informed

investors. By this way, fast arbitrage impairs liquidity because liquidity providers require a

compensation for bearing the risk of being picked off (Copeland & Galai, 1983).2

In addition, to reduce execution risk in trading, arbitrageurs completing with others for

the same trade often use market orders in forming their arbitrage portfolios, subsequently

creating order imbalances. As documented in O’Hara and Oldfield (1986), Chordia, Roll, and

Subrahmanyam (2002), and Roll, Schwartz, and Subrahmanyam (2007), these persistently

created order imbalances raise inventory risk for liquidity suppliers. Therefore, arbitrage

decreases liquidity.

However, liquidity provision is of great importance to financial markets because

illiquidity impedes transactions. Prior literature on the study of arbitrage focuses primarily on

1 In contrast, Holden (1995), Gromb and Vayanos (2002, 2010), and Foucault, Pagano, and Rӧell (2013) find that

arbitrage improves liquidity if arbitrage opportunities stem from transient non-fundamental demand shocks.

2 The barriers to enforce the Law of One Price such as attention costs and technological constraints on traders’

speed are falling as high frequency arbitrageurs invest massively in fast trading technologies to exploit very short-

lived arbitrage opportunities.

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the size of profits and its impact on liquidity. In contrast, such research in liquidity supply as

violating the LOP is still lacking. Furthermore, most studies regarding the supply of liquidity

mainly examine the stock, foreign exchange, and futures markets3 while the liquidity supply

in option market is less well addressed. This paper attempts to fill this gap by exploring the

liquidity provision of option market in the period of arbitrage exploitation.

Over the past years, the electronic limit order market has become one of major trading

venues in equity, futures, and option exchanges around the world. In this trading platform, any

trader is likely to play a role in providing liquidity on the exchange by quoting bid and ask

prices at which he is willing to buy and sell a specific quantity of assets. Moreover, illiquidity

caused by toxic arbitrage impedes transactions and subsequently makes price inefficient. Thus,

understanding the liquidity supply of option market by different trade types in arbitrage shocks

is of high importance because of increased investor interest and regulator concern for this toxic

arbitrage.

This study uncovers who drives option prices to violate the LOP and examines the

liquidity supply by trader types in the period of arbitrage exploitation. In aspects of liquidity

supply of option, we compare the variations in number of orders submitted on the opposite side

of arbitrageurs by each of trader types during times of before and after violating LOP. Also,

we individually perform a panel regression to analyze the liquidity supply by each trader type

controlling on market shocks. Our analysis helps explain who plays a crucial role in providing

liquidity when option market demands liquidity suddenly and further tests whether market

markers fulfill their exchange obligation of liquidity provision at the same time.

In addition, a linkage between submitted limit orders and liquidity of option is also

examined. Chung, Van Ness, and Van Ness (1999) document that the intraday limit-order

3 See, for example, Biais, Hillion, and Spatt (1995), Chung, Van Ness, and Van Ness (1999), Ahn, Bae, and Chan

(2001), Anand, Chakravarty, and Martell (2005), Bjonnes, Rime, and Solheim (2005), Bloomfield, O’Hara, and

Saar (2005), Menkhoff, Osler, and Schmeling (2010), and Chiu, Chung, and Wang (2014).

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spread is significantly related to the intraday variation in limit order placements. A few limit

orders in the book usually accompany with a wider spread. In contrast, a narrower spread is

produced when there are a lot of limit orders. However, in practice, the bid-ask spread is an

indicator of liquidity and directly associated with transaction costs of all market participants.

We further examine the impact of submitted limit orders on liquidity around LOP violations.

Our result provides an additional insight on the variations in liquidity of option established by

submitted limit orders of different trader types.

To guide our empirical analysis, we rely on a simple no-arbitrage relation, the well-known

put-call futures parity (PCFP). It only hinges on the idea that the payoff of a futures contract

can be synthetically replicated using call options, put options, and bonds. In reality, the option

market relies heavily on arbitrage to ensure that prices do not deviate substantially from fair

value for long period of time. Since options with a lot of distinct exercise prices and contract

months are traded simultaneously in the marketplace, the PCFP violations caused by

asynchronous adjustments in option prices should occur more frequently as new information

shocks.4 However, attracted by the potential profits, arbitrageurs responding to the toxic

arbitrage opportunities impair liquidity. Therefore, the PCFP violations provide an ideal venue

to test the liquidity supply of option.

Although option market is dynamically efficient5, numerous empirical studies still report

frequent and substantial violations at short-lived term.6 These price violations from their no-

4 Most literature on price discovery, documented by the speed at which prices react to new information, finds that

index futures lead both index options and the spot index (e.g., Stoll & Whaley, 1990; Fleming, Ostdiek, & Whaley,

1996).

5 Lee and Nayar (1993), and Fung and Chan (1994) find that both the S&P 500 option and futures markets, in

general, are efficient by testing put-call-futures parity using S&P 500 index options and futures contracts. Based

on put-call-futures parity, Fung and Fung (1997), and Fung, Cheng, and Chan (1997) report that markets are

dynamically efficient by using Hong Kong’ Hang Seng Index futures and options.

6 Many empirical studies show that despite the put-call parity usually holds, there are frequent, substantial

violations of put-call parity (Stoll, 1969; Gould and Galai, 1974; Klemkosky and Resnick, 1979; Evnine and Rudd,

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arbitrage values correlate with illiquidity (e.g., Kamara, & Miller, 1995). Motivated by the

commonly recognized fact that liquidity facilitates arbitrage and, in turn, enhances market price

efficiency, we explore who provides liquidity in facilitating arbitrage. Noteworthily, in this

study we only shed light on option market because the futures market is more liquid and high

pricing efficiency relative to option market.7

The empirical work is constructed on analyzing the unique data set with identified trader

types from the Taiwan Index option (TXO) market over almost 2 years. Based on the unique

data, we divide traders by types into four categories: market makers, individual traders, foreign

institutional traders, and domestic institutional traders. Our results complement those in much

of the extant literature, which analyze the data of stock, foreign exchange, and futures markets.

To the best of our knowledge, this paper is the first study to examine the liquidity supply by

trader types in the option market.

Our empirical results provide evidence that option price violations related to the PCFP are

mainly driven by individual traders. In terms of initially violating PCFP, the orders on the

opposite side of arbitrageurs are submitted most by market makers, followed by individual

traders, and least by foreign and domestic institutional traders. The market makers respond

most limit orders centralized on best 5 quotes, but least market orders. In contrast, individual

traders use most of market orders.

For liquidity providing by trader types, we find that market makers dominate the

response of liquidity supply in arbitrage shocks whereas individual traders and domestic

institutional traders respond less. This result is robust even using aggressive orders with highly

executed probability instead of orders submitted. However, our results provides evidence that

1985; Kamara and Miller, 1995). For put-call-futures parity tests, Fung and Mok (2001) find significant arbitrage

profitability by using the quotes of Hang Seng Index options and futures.

7 The liquidity, transaction costs, pricing efficiency, and price discovery in the TXO market have been explored

by Roope and Zurbruegg (2002), Hsieh (2004), Huang (2004), and Chou and Wang (2006). Generally, evidence

confirms that the market of index futures is good in quality in every perspective.

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market markers do their formal market making obligation as option market demands

unexpected liquidity. It also supports the results of Mayhew (2002), and Eldor, Hauser, Pilo,

and Shurki (2006) who find the contribution of market makers to the liquidity in the option

market.

In terms of before and after violating PCFP, the effect of submitted limit orders on

liquidity is different. Overall, an increase in submitted limit orders improves option liquidity

during times of before violating PCFP, consistent with Chung et al. (1999) who find a negative

relation between the number of outstanding limit orders and spread. Inversely, more limit

orders reduce liquidity during times of after violating PCFP, reflecting an unaggressive order

submission by market traders. The evidence supports the result of Kamara and Miller (1995),

Kumar and Seppi (1994), Roll et al. (2007), and Foucault et al. (2014) that arbitrage deteriorates

liquidity. Also, for most of different trader types we find negative relations between submitted

limit orders and liquidity during period of after violating PCFP.

In addition, consistent with most prior studies, we find that market characteristics affect

the order placements of different trader types, like as net buy pressure of option, arbitrage profits,

the volatility and return of futures, option trade volume, and option moneyness.

Our results are related to a recent strand of literature that shows the difference in supply

and use of market liquidity between informed and liquidity traders (or patient and impatient

traders) in the limit order book. These studies are analyzed by both theoretical model such as

Glosten (1994), Chakravarty and Holden (1995), Seppi (1997), Hariss (1998), and Kaniel and

Liu (2006) and by empirical work like as Keim and Madhavan (1995), Bloomfield et al. (2005),

and Foucault, Kadan, and Kandel (2005). In addition, Chiu et al. (2014) find that institutional

traders use more limit orders than market orders in the Taiwan index futures market. Bjonnes

et al. (2005) explore the liquidity supply of non-financial customers in the foreign exchange

market (Swedish Krona market).

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Other related studies focus on investigating whether market characteristics such as spreads,

order size, and depth in the book impact on order placement strategy respectively using both

dynamic model like as Parlour (1998), Foucault (1999), and Foucault, Kadan, and Kandel

(2005)8 and by empirical work like as Biais et al. (1995), Chung et al. (1999), Bae, Jang, and

Park (2003), Menkhoff et al. (2010), and Chiu et al. (2014).9 Besides, Honda and Schwartz

(1996), Ahn et al. (2001), Bloomfield et al. (2005), Menkhoff et al. (2010), and Chiu et al.

(2014) study whether characteristics of underlying asset such as volatility affect the supply of

market liquidity.10

Our study is organized as follows. Section 2 describes the Taiwan option market structure

and presents our data. Section 3 explains our empirical methodology. Section 4 present the

empirical results. Section 5 is robustness tests. Finally, Section 6 provides the key results of the

study and concluding remarks.

8 With dynamic models, Parlour (1998) proposes a “crowding out” effect to examine that traders place less limit

orders when the limit book on the same side of the trade is thicker. This effect arises since the time priority of

orders already in the book reduces the execution probability of a new order on the same side. Foucault (1999)

analyzes the impact of being picked-off risk on traders’ order placement strategy. He finds that limit order traders

widen their bid-ask spreads against losses due to increased probability of being picked-off in terms of high level

of asset volatility. Foucault, Kadan, and Kandel (2005) find that large spreads are more frequent in markets

dominated by impatient traders because these markets are less resilient.

9 Biais et al. (1995) show that investors place limit (market) orders when the spread or market depth is large

(small) in the Paris Bourse. Chung et al. (1999) also find more limit orders submitted by traders when the intraday

spread is wide in New York Stock Exchange (NYSE). Menkhoff et al. (2010) find that informed traders are more

sensitive to change in spreads, order size, and depth than uninformed traders in Moscow Interbank Currency

Exchange. In addition, both Bae et al. (2003) and Chiu et al. (2014) find that spreads, order size, and market depth

have significant and positive impact on trader’s order choice in the NYSE SupperDot and in the Taiwan index

futures market, respectively.

10 Bloomfield et al. (2005) show that volatility affects both informed and uninformed traders’ choice between

limit and market orders. Ahn et al. (2001) study the role of limit orders in the stock Exchange of Hong Kong

(SEHK) and find negative impact from transitory volatility to market depth. Their finding is consistent with Honda

and Schwartz (1996). Menkhoff et al. (2010) and Chiu, Chung, and Wang (2014) find that volatility significally

affect trader’s order choice.

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2. Taiwan index options market structure and sample selection

The TXO option market is a hybrid market like as the NYSE and Amex, in which both market

makers and limit order traders establish prices. The designated market makers in the TXO

option market must reflect in their quotes the highest bid price and the lowest ask price posted

in the limit-order book as they provide the bid and ask price quotations in response to inquiries

by market participants.11

The TXO with European style and Taiwan stock index futures (TX) both traded in Taiwan

Futures Exchange (TAIFEX) share the same underlying asset, the Taiwan Stock Exchange

Capitalization Weighted Stock Index (TAIEX)12, and expiration date, the third Wednesday of the

delivery month of each contract13. The preopen session of TXO and TX is from 8:30 a.m. to 8:45

a.m. During this period, investors can submit orders to the electronic limit-order book, and the

exchange uses the single-price action system to establish the opening prices of regular trading

hours. The regular trading hours conducted on weekdays excluding public holidays are from 8:45

a.m. to 1:45 p.m. (Taipei time). In real time, the TAIEX disseminates order and transaction prices

to the public. Investors can observe on the screen the specific anonymous best five bid and best

five ask prices with the number of contracts.

In our analysis, we use intraday tick-by-tick data of the TXO and TX obtained from the

TAIFEX. The data cover the period from January 1, 2007 to December 31, 2008 and contain

detailed information on consolidated transactions, quotes and order flows, and order book. For

11 Upon receiving the quote request message, a quote is a two-way (bid and ask) limit order placed by a market

maker. His bid-ask spread must be within the range stipulated by TAIFEX, and the quantity ordered (i.e. the

minimum quantity ordered) must comply with relevant requirements as well. In addition, a market maker can also

give a quote without being asked.

12 The TAIEX is a value-weighted index of all common stocks.

13 For the delivery months, the futures contracts are spot month, the next calendar month, and the next three quarterly

months, and the option contracts are spot month, the next two calendar months, and the next two quarterly months.

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each order, the date and time of order submission, order type and quantity, trade direction (buy

or sell), limit price, and trader identification are recorded. The trader identification enables us

to categorize four types of traders: market makers (MM), individual traders (IT), foreign

institutional traders (FIT), and domestic institutional traders (DIT). In addition, the three month

time deposit of the postal saving system, retrieved from TEJ, is used to be a proxy for the risk-

free interest rate.

The source files are checked whether there are typographical problems to avoid large

pricing problem. We also eliminate price limit day, time periods without limit order

information, and days with missing trading data.14

[TABLE 1 ABOUT HERE]

Table 1 presents the order book statistics of call options by trader types from January 1,

2007 to December 31, 2008. Panel A and Panel B show the percentage of the number of orders

submitted by MM, IT, FIT, and DIT in the preopen period and in regular trading period,

respectively. All the order books are divided into the following categories based on quotes:

MO (market order); BB1Q (better best quote), which is the submitted limit orders to the better

best quote; B1Q (best 1 quote), which is the submitted limit orders at the best 1 quote; B2-5Q

(best 2–5 quotes), which refers to the limit orders that are submitted to behind the best 1 quote

but at or before the best 5 quotes; and BB5Q (behind best 5 quote), which means the submitted

limit orders behind the best 5 quote. In addition, we report the total number (TOSN) and total

frequency (TOSF) of submitted orders each trader type. In each row, the numbers in

parentheses represent the percentages of orders in each order type submitted by MM, IT, FIT,

14 Futures data are missing for eight days in June 2008 and three days in December 2008.

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and DIT, respectively. The numbers in brackets for each column are the percentages of order

types by each trader type himself.

In the preopen period, as shown in Panel A, individual traders dominate order submission.

They submit most limit orders and market orders (including bid and ask orders) with the

percentages of 94.74% and 74.29% for all market orders (48,586 contracts) and limit orders

(9,575,724 contracts), respectively.

For the regular trading period, the analysis from Panel B obtains several empirical results.

First, a large portion of posted bid and ask orders is found to originate from market makers. On

average, market markets submit 81.18% of all orders (on both sides of the quote) while

individual traders, foreign institutional traders, and domestic institutional traders are

respectively with the portions of 10.72%, 5.10% and 3.01% of all quote orders. Second,

relatively high proportion of market orders (with 94.03%) is submitted by individual traders

but market makers use little (only with 0.39%).

Next, individual traders are more aggressive while domestic institutional traders are less

aggressive. For each trader type, we calculate the ratio of aggressive orders as the orders with

prices greater than the best 2–5 quotes (i.e., the sum of MO, BB1Q, and B1Q) to all orders by

each trader type himself. The ratios of aggressive orders are 60.02%, 47.13%, 36.60%, and

21.98% separately for IT, MM, FIT, and DIT. The result shows that IT are aggressive. Forth,

market makers submit the largest size of orders about 18 contracts per submission (with being

5, 13, and 10 contracts per submission for IT, FIT, and DIT).


Table 2 reports the order book statistics of put options by trader types. The results are the

same with those in Table 1. Market makers dominate the order book of put options and submit

relatively larger order size than other trader types; in the regular trading period, individual

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traders are aggressive and use a high ratio of market orders.

In addition, we follows the data-matching procedure adopted by Fung and Mok (2001) to

match the futures and options prices within 15-second time interval. Firstly, every bid (ask)

quote of call option is matched with ask (bid) quote of the put option with same exercise price

and maturity. Next, the option pair is then matched with ask (bid) quote of futures contract. To

reduce the impact of illiquid trade on our test results, this study only use the data of spot month

contract. The options and futures with time to maturity less five trade days are switched from

first deferred contracts to nearby contracts.

3. Methodology

3.1 PCFP violation and its size

Tucker (1991) documents that if the European options and futures contracts share the same

underlying asset and expiration, the payoff of a futures position can be synthesized by a call option

and a put option with the same exercise. However, PCFP needs to hold exactly at any point in

time, otherwise investors may benefit from arbitrage trading until the mispricing is eliminated.

The arbitrage profits incorporating the costs are given in Equations (1) and (2), which separately

represent the ask price of futures (,ask tF ) under the bid price of synthesized futures ( ,

syn

bid tF ) and the

bid price of futures (,bid tF ) over the ask price of synthesized futures ( ,

syn

ask tF ).

, , , , ,[( ). ]syn r

bid t ask t bid t ask t ask t t tF F C P e K F M (1)

, , , , ,[( ). ]syn r

bid t ask t bid t ask t bid t t tF F F C P e K M (2)

in which ,bid tC and

,ask tC (,bid tP and

,ask tP ) denote the bid and ask prices of calls (puts) at time t.

,bid tF and,ask tF are the bid and ask prices of futures at time t. K is the option exercise price. τ denotes

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the time to maturity. r is the risk-free interest rate. M and denote the opportunity costs of margin

deposits and trade costs.

The total costs for establishing arbitrage portfolio (i.e., arbitrage costs) consist of

opportunity costs of margin deposits (M)15, and trade costs ( )16. We consider the opportunity

costs (M) since cash is primarily used for margin deposits of options and futures. Following

Fung and Fung (1997), the financing cost on margin deposits is calculated as .( 1)rTMD e , in

which TMD is the total margin deposits.

The trade costs for arbitrage ( ) constructed on the hold-to-expiration strategy involve

the opening trade costs for one pairs of call and put options and a futures contract, and the

settlement costs for a futures contract and an option (call or put)17. No charge is levied for out

of the money options on expiration.

In addition, Equation (1) also implies that a call option is overvalued, a put option is

undervalued, or both. The arbitrage profit in Equation (1) is equivalent to the difference between a

bid price of call and a ask price of synthesized call, and the difference between a bid price of

synthesized put and a ask price of put.18 Moreover, in practice, the speed at which futures prices

react to new information is faster than that of option (Stoll & Whaley, 1990; Fleming, Ostdiek,

15 Fung and Fung (1997) find that the effect is small when differential borrowing and lending rates are used.

16 In the TXO market, transaction tax is 0.025% for the futures contract value, and 0.125% for the option premium.

At expiration, an in-the-money option is subject to 0.025% tax of the settlement value if it is closed out by

settlement instead of by offsetting trading. An out-of-the money option is not taxed because no transaction would

be made. In addition, since settlement price is not available in time t, here we use futures price instead of settlement

price.

17 Because the multipliers for the futures and option contracts are NT$200 and NT$50 per index point,

respectively, every four pairs of calls and puts, thus, can be hedged by one futures (FITX) contract. For

simplification, this study represents the arbitrage profits by NT$50 per index point, consistent with the option’s

multiplier. Therefore, one pair of call and put options is only hedged by one FITX contract. However, despite the

difference in multiplier values, the PCFP condition still holds.

18 Based on the PCFP, a call can be synthesized by long a put, long a futures contract, and short a risk free bond.

Similarly, a put can be synthesized by long a call, long a risk free bond, and short a futures contract.

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& Whaley, 1996). Consequently, the call’s bid price over the ask price of synthesized call and the

put’s ask price under the bid price of synthesized put reflect an overvalued call or an undervalued

put, or both. Similarly, Equation (2) implies an undervalued call or an overvalued put, or both. In

this paper, we analyze the liquidity providing in these four categories of PCFP violations, i.e., call

and put options with overvalued and undervalued prices.


Table 3 reports the statistics of arbitrage profits involved trading costs. Using the option

and futures data from January 1, 2007 to December 31, 2008, there is 0.14% percentage of

option prices to violate the PCFP in all samples. We further divide options violating PCFP into

three groups by call option’s moneyness (myn): for in-the-money options with myn below 0.975

(ITM), at-the-money options with myn above 0.975 and below 1.025 (ATM), and out-of-the-

money options with myn below 1.025 (OTM). The moneyness is calculated as K/(S*erτ), in

which K is exercise price, S is the underlying index price, τ is time to maturity, and r is risk-

free interest rate. The measure unit for arbitrage gain is an index point, with each index point

valued at NT$50.

As shown in Table 3, the arbitrage profit averages 3.5244. On average, the arbitrage profit

for OTM options is slightly above those in ITM and ATM options by about 2 index point,

respectively with average profits of 5.6227, 3.3920, and 3.4083. They are positively skewed

and exhibit leptokurtosis. However, attracted by these potential profits, investors will conduct

their arbitrage trade by rapidly submitting orders to build their arbitrage portfolios.

3.2 Arbitrage toxicity

3.2.1 PCFP violation and its toxicity

Recent studies show that the impact of arbitrage on liquidity depends on the reasons why

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arbitrage opportunity arises. Holden (1995), Gromb and Vayanos (2002, 2010), and Foucault,

Pagano, and Rӧell (2013) find that arbitrage improves liquidity if arbitrage opportunities arise

a result of transient non-fundamental demand shocks, i.e., is non-toxic. Alternatively, arbitrage

opportunities can also stem from asynchronous adjustment in option prices following new

information arrival. As documented in Domowitz, Glen, and Madhavan (1998), Kumar and

Seppi (1994), Foucault, Kozhan, and Tham (2014), these arbitrage opportunities are toxic and

decrease liquidity due to created adverse selection costs for liquidity providers.

Inspired by Schultz and Shive (2010), we identify toxic arbitrage opportunities as situations

in which asynchronous adjustment in option prices are eventually followed by permanent shifts

in futures prices.19 The non-toxic arbitrage opportunities are followed by reversals in futures

price initially the arbitrage opportunity. More specifically, we consider that an arbitrage

opportunity is non-toxic if the futures price change at the origin of this opportunity reverts after

the opportunity terminates. If instead this price change of futures persists after the arbitrage

opportunity terminates, we consider that the arbitrage opportunity is toxic due to asynchronous

adjustments in option prices.

Figure 1 shows the plot of correlation coefficients between the return of index futures at 15-

second (30-second) time interval of just violating PCFP at time t=0 and the cumulative index

futures return from time t=0 to the tth time interval of after violating PCFP, in which t=1, 2, …, 12

(2, 4, …, 12) for 15-second (30-second) time intervals. A positive (negative) correlation coefficient

indicates that the price in index futures moves in the same (opposite) direction before and after

violating PCFP.

19 As an illustration, suppose that liquidity providers in the futures market receive a string of buy orders due to

good information arrival and raise their bid and ask quotes. If this price move is large enough and liquidity

providers in the option market are slow to adjust their quotes to reflect this information, then an arbitrage

opportunity in PCFP violation appears. When arbitrage opportunity vanishes, the futures prices do not revert to

their position before the arbitrage opportunity because the initial shock is a shock to fundamentals.

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[FIGURE 1 ABOUT HERE]

A visual inspection shows that both the correlation coefficients for 15- and 30-second time

intervals decrease gradually over time and are all positive with significance at 1% level. During

times of arbitrage shocks, the correlation coefficients for 15-second (30-second) time intervals

range from 0.41 to 0.80 (0.5 to 0.79), suggesting that arbitrage opportunities in PCFP violations

are inclined to be generated by asynchronous adjustments in option prices. In addition, for each

PCF violation, we compare the futures prices at the onset of arbitrage opportunity (time t=0)

and at time t=1, 2, 3, and 4. If the move direction of future price is same, we regard it as a toxic

arbitrage opportunity. Our analysis reveals that on average, the fractions of toxic arbitrage

opportunities over all PCFP violations are 67.07%, 63.39%, 60.58%, and 58.00% (72.83%,

69.29%, 62.00%, and 59.67%) in 1st, 2nd, 3rd, and 4th time intervals of 15 seconds (30 seconds)

of after violating PCFP. However, these results support that PCFP violations are toxic arbitrage

opportunities.

3.2.2 Order imbalances on quote and trade

If mispriced options may be observed by market investors using a simple PCFP, then their new

quotes for the potential profits will cluster in a direction of arbitrage trade. This leads newly

submitted bid-ask orders of options to imbalance. In addition, to reduce execution risk in

trading, arbitrageurs who complete with others for the same trade submit more aggressive

orders in forming their arbitrage portfolios. These imbalanced quotes on more aggressive

orders may create order imbalances on trade. As documented in O’Hara and Oldfield (1986),

Chordia et al. (2002), and Roll, et al. (2007), these persistently created order imbalances raise

inventory risk for liquidity suppliers. Arbitrage, thus, decreases liquidity

As exhibited in Panel A of Table 4, in 15-second time interval of initial arbitrage shocks,

the ratios of cumulative average number of submitted bid orders to ask orders by quote types

16

(A/B) are almost less than one for overvalued calls and puts, but almost greater than one for

undervalued options. This provides empirical evidence in favor of that arbitrage introduces

newly submitted bid-ask order imbalances.

More specifically, the largest difference between cumulative bid and ask orders, reported

in columns of Cum. (A) and Cum. (B), occurs at best quote, B1Q (e.g., with the averages of -

2.56 and -33.83 contracts separately for overvalued calls and puts). The asymmetric number of

bid-ask orders clustering on the prices better than the best 2–5 quotes reflects that market

participants place unaggressive orders in the side of liquidity supply during times of arbitrage

shocks. Besides, on the side of arbitrageurs we find more aggressive ask (bid) orders in MO

and BB1Q for overvalued (undervalued) options. These aggressively asymmetric quotes may

create order imbalances on trade since these two quote types of MO and BB1Q are almost

executed immediately.


Similarly, Panel B reported a 30-second time interval of initially violating PCFP also

obtain same results. However, the results above suggest that overvalued (undervalued) options

generates more ask (bid) orders than bid (ask) orders and results in order imbalances on trade,

as shown in Figure 2.


Figure 2 shows the average excess order imbalances (AEOIB) of mispriced options during

the 12 successive time intervals of 15 seconds after violating PCFP (at time t=0). The PCFP

violations are divided into four categories: overvalued calls, overvalued puts, undervalued calls

and undervalued puts. For the AEOIB of each category in each 15-second interval, we first

17

calculate the AEOIB and then average them. The AEOIB is calculated as order imbalance less

the mean of order imbalances in 360 successive time intervals of 15 seconds prior to the

occurrence of arbitrage opportunity. For the order imbalances, they are computed over all

trades within each time interval. Following the Lee and Ready’s (1991) algorithm, we calculate

order imbalance as buyer-initiated trades less seller-initiated trades,

In Figure 2, we find negative (positive) AEOIB for overvalued (undervalued) options after

PCFP is violated. The magnitude of AEOIB increases at first 15-second time interval, and

decreases until the fourth 15-second time interval, then level off. This suggests that arbitrage

generates persistent order imbalances due to completing with others for the same trade. The

negative (positive) AEOIB for overvalued (undervalued) options reflects a trade direction on

sell (buy) side, consistent with that of arbitrageurs. Also, it suggests that liquidity suppliers

absorbed imbalances on buy (sell) side cannot adjust their inventories easily during period of

arbitrage shocks.20

However, order imbalances have a contemporaneous and persistent impact on liquidity

(Stoll, 1978; O’Hara & Oldfield, 1986; Chordia et al., 2002). This persistence on order

imbalances in either buy or sell side may raise the inventory risk for liquidity suppliers,

subsequently impairing liquidity. Since liquidity is reduced, thus arbitrage opportunities in the

PCFP violations are toxic.

3.3 Liquidity providing in PCFP violations by trader types

Arbitraging in PCFP violations decreases liquidity. A liquidity provider should be who

provides more bid (ask) quotes in the option order book when option prices are overvalued

(undervalued). This is because that more orders placed on the opposite side of arbitrageurs may

raise the execution probability of orders (Chung et al., 1999), i.e., increasing liquidity supply.

20 The order imbalances can be used to measure both direction and degree of buying or selling pressure (Chordia

et al., 2002; Chordia & Subrahmanyam, 2004).

18

As a result, we define the supply of liquidity during times of arbitrage shocks as an increase in bid

(ask) orders for overvalued (undervalued) options.

This study particularly interests in liquidity supply of option during period of arbitrage

exploitation. However, in practice, arbitrage opportunity is short-lived. For each violation, we

select the option data within before and after 3-minute time period of violating PCFP (i.e., 24

successive time intervals of 15 second) as data set to test liquidity supply by different trader types.21

Furthermore, the violations with less than three successive time intervals of 15 seconds in before

or after of violating PCFP are excluded from the sample (i.e., violations occurs in before

8:45:30 a.m. or after 1:44: 30 p.m.).

Our empirical analysis for liquidity supply to option market are in two ways. First, we

analyze the percentage of change in the number of orders submitted by each trader type on the

opposite side of arbitrageurs just before and after violating PCFP.

Second, we adopt an unbalanced panel regression to analyze the variation in the number of

bid (ask) orders, NLMt, of overvalued (undervalued) options. For each trader type and each type

of PCFP violations, options (calls and puts) with overvalued and undervalued prices, we

individually use the panel regression to investigate the supply of liquidity. In addition, the

Hausman test statistic (1978) with asymptotical chi-squared distribution (χ2) is used to

differentiate between fixed effect model and random effect model in panel data. A rejection of

the null hypothesis indicates that the fixed effect model is suitable for the panel data. The empirical

model is specified as

21 Cheng, Fung and Pang (1998) find that arbitrage profitability, based on the PCFP, declines and subsequently

disappears within 5 minutes. Fung and Draper (1999) analyze the mispricing of the Hong Kong Seng Index. They

find that arbitrage profit opportunities exist within 5 minutes and become smaller or disappear as the time lags

increase. Consequently, here we use the average value of 3 minutes.

19

, 1 , 1 2 1 3 , 1 4 1 5 , 1

12

6 , 1 7 , 1 8 , 1 9 ,

1

* * * * *

* * * * *

i t i t t i t t i t

i t i t i t i t j j,t t

j

NLM NBP RV ArbSz FRet OVol

OSpd TolBid TolAsk Myn D

,i = 1,2,3,...,N, t = -a,...,0,...,b, and a,b [3,12]

(3)

The dependent variable, tNLM , denotes the number of bid (ask) orders submitted on the

opposite side of arbitrageurs for overvalued (undervalued) options during t time interval. N is the

number of PCFP violations. The time interval t=0 indicates the occurrence of violating PCFP. t

is the error term. tMyn is option moneyness at time t.,j tD is a dummy variable that equals 1 if it is

in jth time interval of after violating PCFP, j=1,2,3,…, 12. This variable captures the intraday

variation in the number of submitted orders with respect to the time of after violating PCFP. The

coefficient of i represents the difference between the mean of ith time interval and the mean of

around the violations of PCFP. The other independent variables associated with market

characteristics are specified as following.

1tNBP indicates option net buy pressure during t-1 time interval, which is measured in terms of

the degree and direction of transaction (Chordia et al., 2002; Chordia & Subrahmanyam, 2004).

The more NBP is often accompanied by a buy transaction due to its persistence (Chordia et al,

2002), suggesting that investors tend to submit bid orders rather than ask orders following a positive

and large NBP. We calculate the NBP as the buyer-initialed trades less the seller-initialed trades

during the t-1 time interval, in which every transaction is assigned using the Lee and Ready (1991)

algorithm.

1tRV is the realized volatility of futures, which is calculated as the square root of the sum of

squared return during t-1 time interval. Handa and Schwattz (1996), Foucault (1999), Ahn et al.

(2001), Bae et al. (2003), Goettler et al. (2005), and Menkhoff et al. (2010) find that price

20

volatility affects order placement and execution. A rise in volatility is followed by an increase

in the order placement and execution. We use the realized volatility to control the dynamic impact

of volatility on order submission.

1tArbSz is the size of arbitrage profits, shown in Equations (1) and (2), at time t-1. In practice,

large arbitrage profits can attract more arbitrageurs, thereby generating more imbalance

between newly submitted bid orders and ask orders. This suggests that the size of deviations

from PCFP is associated with order placement strategy. We thus use this variable to control the

impact of PCFP deviation on order submission.

1tOSpd denotes the average best bid-ask spread of options during t-1 time interval, which the

literature finds significant response of order placement to changes in spreads (Bae et al., 2003;

Biais et al., 1995; Chung et al., 1999; Menkhoff et al., 2010). It is used to control for the effect

of option spreads on order submission.

1tTolBid and 1tTolAsk are the average of bid and ask volume submitted at the best 5 quotes

during the t-1 time interval, respectively. Numerous studies document that changes on depth in the

buy and sell sides of the book affects order submission (Menkhoff et al, 2010; Ranaldo, 2004).

A rise in the same side depth of the trade discourages the limit order at the same side depth while

encouraging the limit order in the opposite side. Thereby, we use this variable to control the impact

of market depth in the book on order submission.

1tFRet and 1tOVol are the return of futures and trade volume of option during t-1 time period,

respectively. We include these two variables due to the probable influence on order submission.

3.4 The impact of limit orders on liquidity

In the marketplace, the intraday pattern of limit-order spread is driven by limit-order quotes of

different traders throughout the day. A few limit orders in the book usually accompanies with

21

a wider spread. In contrast, a narrower spread is generated when there are a lot of limit orders

in the book. Chung et al. (1999) document that the intraday limit-order spread is determined

by the number of outstanding limit orders (i.e., adding the number of newly placed limit orders

to outstanding limit orders at the end of prior time interval and then subtracting the number of

executed limit orders). This suggests that liquidity, widely measured by quote spread, is related

to the number of new order placement.

However, in practice, the bid-ask spread is an indicator of liquidity and directly associated

with transaction costs of all market participants. We further examine the variation in liquidity

of options established by submitted limit orders (NLO) of different trader types around PCFP

violations. We employ the following unbalanced panel regression as an empirical investigation on

the impact of limit orders on liquidity. For each trade type and each type of PCFP violations, we

estimate the panel regression controlling on trade volume of option (OVol ) and liquidity at prior

time interval.M,tD is a dummy variable that equals 1 if it is in 12 successive time intervals of 15

seconds of after violating PCFP.

In addition, the negative (positive) 1 indicates that liquidity rises (falls) following increased

limit orders during times of before violating PCFP. A negative (positive) sum of 1 and 2 shows

that increased limit orders narrow (widen) the percentage spread during times of after violating

PCFP.

i,t 1 i,t 2 M,t i,t 3 i,t 4 i,t-1 tLiq = α+ β * NLO + β * D * NLO + β * OVol + β * Liq +ε

,i = 1,2,3,...,N, t = -a,...,0,...,b, and a,b [3,12] (4)

where tLiq is the liquidity of option at the end of time interval t, which is measured as bid-ask

spread divided by the midpoint of quote. N is the number of PCFP violations. tNLO is the

22

number of newly submitted limit bid and ask orders during time t interval (i.e., the sum of bid

and ask orders in quote types of B1Q, B2-5Q, and BB5Q). tOVol is the option trade volume

during time t interval.

The coefficients in Equation (4) are estimated using the two stages least square (2SLS)

panel regression due to possibly endogenous problem between liquidity, submitted limit orders,

and trade volume.22 In the process of calculating the estimates, we use lagged values of number

of submitted limit orders (NLO), trade volume (OVol), realized volatility (RV), net buy pressure

(NBP), arbitrage size (ArbSz), and return of futures (FRet) as instrument variables.

4. Empirical Results

4.1 Who drives option prices to violate the PCF parity?

An interesting and important question arising from temporary mispricing of options is who

drives option prices to violate the PCFP. Bollen and Whaley (2004), Ni, Pan, Poteshman (2008),

and Gârleanu, Pedersen, and Poteshman (2009) document that the net buy (sell) demand drives

option price upward (downward). Following their argument, we use the net buy volume of

options by each trader type to investigate this issue, which is constructed on 24 successive time

intervals of 15 seconds before and after violating PCFP (at time t=0). For each time interval,

we calculate average net buy volumes of mispriced options, measured by buy volume less sell

volume, by each of trade types. The results are exhibited in Figure 3.


22 Chung et al. (1999) argue that there exists an endogenous problem between the limit order spread, the quantity

of limit orders, and the execution rate of limit orders.

23

Figure 3 shows the plot of average net buy volume of options by trader types around PCFP

violations. Figures A and D (C and B) represent the average net buy volumes by each trader

type separately for overvalued (undervalued) calls and puts. For overvalued options (shown in

Figures A and D), we find an increasing net buy volume for individual traders but an increasing

net sell volume for market makers prior to PCFP violations. Inversely, individual investors for

undervalued options (shown in Figures C and B) have an increasing net sell volume, while

market makers have an increasing net buy volume. For individual traders, the corresponding t-

values from t=-4 to t=2 are 2.02, 2.00, 5.34, 10.46, 18.50, 16.72, and 3.13 (-5.40, -3.66, -3.89,

-13.44, -15.57, -11.60, and -3.20) on the overvalued (undervalued) calls, and 6.83, 7.33, 7.58,

9.00, 10.48, 9.62, and 6.13 (-19.49, -19.98, -21.86, -23.08, -26.74, -27.88, and -22.05) on the

overvalued (undervalued) puts, respectively.23 Besides, regardless of overvalued options and

undervalued options, the net buy volumes of foreign and domestic institutional investors are

almost invariant around PCFP violations.

The finding that the process of option price to violate the PCFP accompanies with

increased net buy (or sell) volume of non-market makers is consistent with Bollen and Whaley

(2004), Gârleanu et al. (2009), and Ni et al. (2008) who document that option net buy (sell)

demand of non-market makers increases (decreases) its price. However, these results provide

evidence supporting that individual traders drive option prices to violate the PCFP.

4.2 Liquidity provision by trader types

Prior to the analysis of liquidity supply by the change ratios of submitted orders and the panel

regression, we first take a look at Table 4 about orders submitted on the side of liquidity supply

23 For market makers, the corresponding t-values from t=-2 to t=2 are 9.33, 8.44, 5.42, 1.37, -7.21, -3.93, and

8.13 (7.45, 6.14, 5.18, 12.14, 14.42, 11.38, and 3.8), respectively, for overvalued (undervalued) calls, and -7.35,

-7.55, -7.97, -10.19, -11.35, -11.02, and -7.49 (10.73, 8.67, 11.94, 15.15, 20.75, 22.53, and 14.50) for overvalued

(undervalued) puts.

24

in terms of initially violating PCFP. In Panel A, we find that, on the whole, investors who face

arbitrage shocks in initial interval of 15 seconds favor to use orders with prices at best 5 quotes

while using a little market orders. This is evidenced by submitted orders clustering at best 2–5

quotes or best quotes, but least for market orders. For instance, the ratios of orders submitted

at best 5 quotes (market orders) to all quoted orders are 59.82% and 53.28% (1.64% and 0.59%)

for overvalued calls and puts.

Regarding the orders submitted by trader types, the untabulated results reveal that the

orders on the side of liquidity supply are submitted most by market makers, followed by

individual traders, and least by foreign and domestic institutional traders. For example, the

submitted bid orders of overvalued calls (puts) average 18.15, 9.15, 2.19, and 0.42 (49.12, 4.33,

3.11, and 2.50) respectively for MM, IT, FIT, and DIT. In contrast, the market orders are

submitted most by IT, but rarely used by MM and FIT.

Also, we compare the order aggressiveness of trader types by calculating the ratio of

orders over best quote to all orders which are submitted by each trader type itself. We find that

IT are aggressive relative to MM. This is because IT have the largest ratios respectively with

the ratios being 29.56% and 40.74% (33.04% and 39.24%) for overvalued (undervalued) calls

and puts whereas the ratios are small for MM with 17.29% and 7.96% (9.69% and 26.61%) for

overvalued (undervalued) calls and puts, respectively.

In addition, Panel B reported a 30-second time interval of initial arbitrage shocks also

obtains similar results. The same findings in Panels A and B that market makers place most

orders within the best 5 quotes but least market orders suggests that market makers seemly act

like a role of liquidity trader who favors to place limit orders.

4.2.1 The percentage of change in the number of submitted orders

At the beginning, we use the ratios of change in submitted orders on the opposite side of

arbitrageurs to measure the liquidity supply in arbitrage shocks. For each type of PCFP

25

violations and each trader type, we compute the ratios of change in submitted orders

accumulated by quote types, which are defined as the difference between average numbers of

submitted orders accumulated by quote types to average numbers of all orders submitted at

prior time interval of violating PCFP. More specifically, we first calculate the differences

between cumulative numbers of submitted orders by quote types in two time intervals of just

before and after violating PCFP and average them. Then, they are divided by the average

number of all orders submitted in one time interval of just before violating PCFP. However,

the advantages of using this measure do not only reflect the change of liquidity supply but also

order aggressiveness.

The results are reported in Table 5. Panel A and Panel B respectively present the results

of mispriced options in two 15-second time intervals and in two 30-second time intervals of

just before and after violating PCFP.


Panel A shows that the ratios at BB5Q, i.e., indicating a percentage change in the number

of all submitted orders, for MM are almost positive with values of 1.1%, 2.29%, and 0.09%

separately for overvalued puts, and undervalued calls and puts, except the overvalued calls with

value of -0.54%. But, the ratios at BB5Q for IT, FIT, and DIT are almost negative, especially

for IT. In contrast to other trader types, the increased ratio for MM indicates that more orders

on the side of liquidity supply are placed by MM in arbitrage shocks.

Specifically, the ratios for maker makers raise in quote types with high level of execution

probability and switch to decrease afterward. The largest ratios of an increase in submitted

orders occurs at best quote (B1Q) with values of 1.52% and 10.97% for overvalued calls and

puts and with values of 10.14% and 2.45% for undervalued calls and puts. This indicates that

market makers place more orders with highly executed probability relative to those submitted

26

at the prior time interval of violating PCFP. The evidence of an increase in use of aggressively-

priced orders supports that market makers provide liquidity to option market in arbitrage shocks.

The results in Panel B for a 30-second time interval of initial arbitrage shocks are also

similar to those in Panel A. Market makers still place more aggressive orders, but individual

traders cut down their submitted orders. Consequently, we conclude that market makers

dominate the response of liquidity supply to arbitrage shocks while individual traders respond

little.

To further test whether market markers do their formal market making obligation as

violating PCFP, we divide the options violating the PCFP into three groups based on the

moneyness of option : for OTM, ATM, and ITM options. Then, for each of PCFP violations

and each trader type, we recalculate the change ratios of submitted orders by each moneyness

group. Here, only the results during period of initial 15-second arbitrage shocks are plotted in

Figure 4: Figures A-C for overvalued calls (OC), Figures D-F for undervalued calls (UC),

Figures G-I for overvalued put (OP), and Figures J-L for undervalued puts (UP). In the x-axis,

the number 1, 2, 3, 4, and 5 respectively correspond to the MO, BB1Q, B1Q, B2-5Q, and BB5Q

of quote types, which are arranged in highly executed probability order.


Figure 4 exhibits the plot of the change ratios of orders submitted by trader types for

different moneyness groups. A visual inspection shows that the ratios for market makers vary

enormously, but the variations in orders submitted by other trader types are relatively small.

The change ratios for market makers in three moneyness groups and four types of PCFP

violations are all positive at best quote (corresponding to the number 3 in the x-axis) and almost

positive at behind best 5 quote (corresponding to the number 5 in the x-axis). More specifically,

the OTM and ATM options have large change ratios of submitted orders. In contrast, the orders

27

submitted by individual traders are generally reduced more in initial arbitrage shocks,

especially for ATM options.

The similar results are obtained in the initial 30-second time interval of arbitrage shocks

(unreported). However, regardless of option moneyness and types of PCFP violations, the

finding that market makers place more orders on the opposite side of arbitrageurs and with

highly executed probability provides in support of liquidity supply by market makers as option

market demands unexpected liquidity.

4.2.2 The results of panel regression analysis

The second way to analyze the supply of liquidity is the panel regression in Equation (3), which

examines the variation in number of submitted orders by incorporating dummy variables. The

dummy variables are used to capture the intraday variation in number of submitted orders with

respect to the time intervals of after violating PCFP. A positive coefficient j of dummy variable

represents an increase in number of submitted orders on the jth time interval of arbitrage shocks.

Inversely, the negative coefficient indicates less orders submitted. The regression results for

overvalued and undervalued options (calls and puts) are reported in Tables 6-9, respectively.


Table 6 and Table 7 present the regression results of liquidity supply on buy side by each

trader type separately for overvalued calls and puts, controlling on market shocks such as net buy

pressure, volatility, arbitrage size, option spreads, futures return, and depth in the book. The results

of the Hausman test (1978) reported in the second row of Tables 6 and 7 show that the fixed effect

model is suitable for the panel data in every trader type. For the liquidity supply by all traders,

in Table 7 we find significant evidence in support of an increase in number of submitted orders

28

on the overvalued puts in first two time intervals of arbitrage shocks (with t-values of 4.59 and

2.92, respectively), whereas no evidence in Table 6 supports an increase in the number of

submitted orders for overvalued calls.

For the liquidity providing in overvalued calls by trader types, however, in Table 6 we

find significant and positive coefficient of D1 for market makers (t-value = 2.06), but almost

significantly negative coefficients for individual traders. In Table 7, we also find that market

makers have two positive coefficients of D1 and D2 for overvalued puts with significance at 1%

level in first two time intervals of arbitrage shocks (t-values = 5.79 and 2.88, respectively). For

individual traders, we find only a significantly positive coefficient of D2 (t-value =1.86) but

significantly negative coefficients in the latter time intervals of arbitrage shocks. These results

indicate that market makers submit more orders of calls and puts and then switch to usual or

less orders afterwards in response to initial arbitrage shocks. In contrast, individual traders

submit less orders except increased orders of puts in the second time interval of after violating

PCFP.

In addition, both the coefficients of dummy variables for foreign and domestic institutional

traders are insignificant (see Table 6) or significantly negative (see the results in Table 7 for

domestic institutional traders). Therefore, we conclude that market makers dominate the liquidity

supply during times of after violating PCFP.


We further specify the effect of market shocks on order submission by each of trader types

from Tables 6-7. For option net buy pressure ( NBP ), all the coefficients are positive and most of

them are statistically significant at 1% level, indicating that more bid orders are submitted by

investors following an increased NBP. This evidence provides in support of the results of Chordia

et al. (2002) and Chordia and Subrahmanyam (2004) that large NBP often accompanies with a

29

buy transaction due to its persistence. Overall, we find that more orders are placed following a

rising volatility evidenced by that the coefficients of realized volatility (RV) for all traders and

most trader types are positive and highly significant at the 1% level. This finding is consistent

with results in Handa and Schwattz (1996), Foucault (1999), Ahn et al. (2001), Bae et al. (2003),

Goettler et al. (2005), and Menkhoff et al. (2010).

For the potential arbitrage profits (ArbSz), the coefficients with negative and highly

significant at the 1% level show that large arbitrage profits stemming from overestimated

options (calls and puts) attract market traders to place more ask orders, thus leading less bid

orders submitted, i.e., on the opposite side of arbitrageurs.

Regarding the depth at best 5 quotes of bids (TolBid ) on same side of liquidity supply, most

of the coefficients for overvalued calls and puts lagged one period are found to have significant and

negative signs. The result indicates that most traders place fewer orders on buy side when the state

of the buy side order book is thicker and more orders when the buy side order book is thinner. This

provides evidence in support of the crowding-out effect proposed by Parlour (1998) who

documents that a rise in the same side depth discourages the orders submitted at the same side depth.

This is because the orders with time priority already in the book lessens the execution probability

of a new order on the same side. In contrast, the effect of the sell side order book (TolAsk ) on

order submission is ambiguous.

On the whole, lagged one-period return of futures ( FRet ) as well as trade volume of option

(OVol ) has a positive impact on bid order placement. One possible explanation is that investors

favor to buy calls and hedgers tend to buy puts when a price of underlying futures rises, and large

trade volume reflecting the quantity of option contracts bought and sold at the same time

accompanies with more quotes in the book (Cohen, Maier, Schwartz, & Whitcomb, 1981; Chung

et al., 1999). As a consequence, this leads to an increase in bid orders of calls and puts. Furthermore,

for all traders and most trader types, we find significantly negative relation between option spread

30

( OSpd ) and order placement, indicating that traders place less orders on the same side of

liquidity supply when intraday spread is wide.

In addition, order submission is associated with option moneyness. One possibility is that

options with different degree of moneyness have distinct financial leverage (risk), hedging ratio,

and liquidity risk (transaction costs) which in turn are correlated with the trading activity. In

general, the newly submitted orders decreases with increased option moneyness ( Myn ). An out-

of-the-money option (calls and puts) tends to decrease orders submitted while an in-the-money

option (calls and puts) increases order submission.


The empirical analysis of liquidity supply on sell side of undervalued calls and puts, reported

in Table 8 and Table 9, obtains several similar results with those in Tables 6-7. In brief, market

makers still provide the liquidity to option market in the session of arbitrage shocks. Our

finding supports the result of Mayhew (2002), and Eldor et al. (2006) who find the contribution

of market makers to the liquidity in the option market.


4.3 The impact of submitted orders on liquidity

Table 10 gives the results of the impact of limit orders (NLO) on liquidity by each trader type

around violating PCFP. Panels A-D report the results for overvalued calls, overvalued puts,

undervalued calls, and undervalued puts, respectively. During times of before violating PCFP,

our results reveal that, in general, an increase in limit orders submitted by all market traders

improves liquidity evidenced by the significantly negative coefficients of NLO (respectively with

t-values of -4.04, -6.18, and -4.10 for overvalued puts and undervalued calls and puts), except for

31

overvalued calls. This result supports the finding of Chung et al. (1999) who find a negative

relation between the number of outstanding limit orders and spreads.

Furthermore, the effect of limit orders submitted by different trade types on liquidity is

likely to be distinct in different types of PCFP violations. In four types of PCFP violations, we

find that both market makers and domestic institutional traders have three significant and

negative coefficients of NLO while individual and foreign institutional traders have two

significantly negative coefficients of NLO, respectively. This suggests that market makers and

domestic institutional traders play a crucial role to narrow the spread of options during times

of before violating PCFP.

In the time intervals of after violations of PCFP, we find that the coefficients of D*NLO

for market traders are all positive and significance at 1% level in four types of PCFP violations.

Specifically, the sum of coefficients for NLO and D*NLO are all positive with 0.00005 and

0.00013 (0.00009 and 0.00007) for overvalued (undervalued) callas and puts, showing that

liquidity of option is reduced as increasing limit orders. These results also reflect an

unaggressive order submission strategy by market traders. However, this evidence provides

support for the results of Copeland and Galai (1983), Kumar and Seppi (1994), Kamara and

Miller (1995), Roll et al. (2007), and Foucault et al. (2014) that arbitrage deteriorates liquidity.


In addition, we also find that the negative relation between liquidity and newly submitted

limit orders almost holds for four trader types during times of after violating PCFP. Only the

limit orders placed by individual and foreign institutional traders are found to reduce the width

of spreads when call or put options are overestimated.

5. Robustness tests

32

In practice, the duration of arbitrage opportunities is short-lived and arbitrageurs face execution

risk in forming their arbitrage portfolios (Kleidon, 1992; Kumar & Seppi, 1994; Holden, 1995;

Kozhan & Tham, 2012). A high speed of trade execution is beneficial for traders to build their

arbitrage portfolios and lowers their execution risk. Therefore, more active orders placed on

the opposite side of arbitrageurs and with high execution probability may stimulate arbitrage

activity and in turn remove mispricing.

To test the robustness of our empirical results, we redefine a provider of liquidity as a

trader who places more active orders with highly executed probability on the opposite side of

arbitrageurs. We use the number of submitted orders available at over best quote, i.e., market

order (MO) and better best quote (BB1Q), instead of the number of all submitted orders. These

orders are executed rapidly in the marketplace. Further, we also re-perform the unbalanced

panel regression in Equation (3) to investigate the supply of liquidity by each trader type.

To save space, we only report the coefficients of dummy variables for mispriced options

in Table 11. Panels A-D represent the results separately for overvalued calls, overvalued puts,

undervalued calls, and undervalued puts.


For overvalued calls and puts, as reported in Panels A and B, we find that the significance

of dummy variables (D1–D12) for market markets are comparable to the results in Table 6 and

Table 7, with calls being significant for D7 and D8 and puts being significant for D1, D2, D6,

D9, and D10. Results support that market makers respond more active orders during times of

after violating PCFP. Similarly, in Panels C and D we also find similar results for undervalued

calls and puts. We thus conclude that market makers play a significant role in providing

liquidity when option market demands unexpected liquidity, supporting that they fulfill their

exchange obligation of liquidity provision.

33

6. Conclusion

Arbitraging in put-call futures parity (PCFP) violations impairs liquidity due to created adverse

select costs and order imbalances. This study investigates the liquidity supply of option

providing in arbitrage exploitation. We use a unique data set of the Taiwan index option to

separately examine the liquidity supply by market makers, individual traders, and foreign and

domestic institutional traders. The data set includes order codes of identification, trading

activity, and the real-time information in order book. Thus, our study is not subject to the trader-

type error.

Our conclusions are specified as follows. First, individual traders play an important role

in driving option prices to violate the PCFP. Second, in terms of initially violating PCFP, the

orders on the side of liquidity supply are submitted most by market makers, followed by

individual traders, and least by foreign and domestic institutional traders. Third, we find that

market makers dominate the response of liquidity supply during times of after violating PCFP

while individual and domestic institutional traders respond less. This finding provides evidence

that market markers fulfill their obligation of liquidity supply when option market demands

liquidity unexpectedly.

Next, for the effect of limit orders on liquidity, we find that on the whole, increased limit

orders improves liquidity during period of before violating PCFP, consistent with Chung et al.

(1999). Inversely, more submitted limit orders reduce liquidity during times of arbitrage

exploitation. This evidence provides in favor of the results of Kamara and Miller (1995),

Kumar and Seppi (1994), Roll et al. (2007), and Foucault et al, (2014) that arbitrage deteriorates

liquidity. Finally, the characteristics of market and underlying asset affect the order placement

strategy by different trader types.

34

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38

Figure 1. Correlation between the returns of index futures before and after violating PCFP. This figure depicts

the correlation coefficient between the return of index futures at 15-second (30-second) time interval of just violating

PCFP at time t=0 and the cumulative index futures return from time t=0 to the jth time interval of after violating PCFP,

in which j=1, 2, …, 12 (2, 4, …, 12) for 15-second (30-second) time intervals. The correlation coefficients are used to

judge whether the price in index futures moves in the same direction before and after violating PCFP.

39

Figure 2. Average excess order imbalances of options after violating PCFP. This figure depicts the average

excess order imbalances (AEOIB) of mispriced options during the 12 successive intervals of 15 seconds after

violating PCFP (at time t=0). The PCFP violations are divided into four categories: for overvalued calls,

overvalued puts, undervalued calls and undervalued puts. For the AEOIB in each time interval of 15 seconds for

overvalued calls (overvalued puts, undervalued calls, and undervalued), we first calculate the AEOIB and then

average them by each time interval. The AEOIB is calculated as the order imbalance less the mean of order

imbalances in 360 successive time intervals of 15 seconds prior to the occurrence of arbitrage opportunity. We

compute the order imbalances over all trades within each time interval. Following the Lee and Ready’s (1991)

algorithm, the order imbalance is measured as buyer-initiated trades less seller-initiated trades.

40

Figure 2. Average net buy volume of options around PCFP violations. This figure depicts the average net buy

volumes of calls and puts by trader types within before and after 3-minute time intervals (24 successive 15-second

time intervals) as arbitrage opportunities occur (at time t=0). The PCFP violations are divided into four classes,

overvalued call and put options and undervalued call and put options. Figures A and D (C and B) show the average

net buy volumes of overvalued (undervalued) calls and puts, respectively, around PCFP violations. For each of

24 time intervals, the average net buy volumes, defined as buy volume less sell volume, are calculated by trader

types.

41

Figure 3. Change ratios of order submission for different moneyness groups. This figure depicts the ratios of

change in submitted orders accumulated by quote types for different moneyness groups during two 15-second

time intervals of just before and after violating PCFP. The numbers 1, 2, 3, 4, and 5 in the x-axis respectively

correspond to the MO, BB1Q, B1Q, B2-5Q, and BB5Q of quote types. The quoted orders are selected on the

opposite trade direction of arbitrageurs and divided into the following categories: MO (market order), BB1Q

(better best quote), B1Q (best 1 quote), B2-5Q (best 2–5 quotes), and BB5Q (behind best 5 quotes). The order

types are arranged in highly executed probability order. For each of overvalued calls (OC), undervalued calls

(UC), overvalued puts (OP), and undervalued puts (UP), they are divided into three groups by option moneyness,

42

including in-the-money options, at-the-money options, and out-the-money options. For each of PCFP violations

and each trader type, we compute the change ratios of submitted orders each moneyness group.

43

Table 1: Order book statistics of call options by trader type categories

MM IT FIT DIT TOSN

Panel A: Percentage of the number of orders submitted by trader types in the pre-open period

MO (1.54%) (94.74%) (1.98%) (1.73%) 48,586 (100%)

[0.04%] [0.64%] [0.17%] [0.43%] [0.50%]

Limit

Order

(17.89%) (74.29%) (5.78%) (2.03%) 9,575,724 (100%)

[99.96%] [99.36%] [99.83%] [99.57%] [99.50%]

TOSN

1,714,101 7,160,261 554,666 195,282 9,624,310

(17.81%) (74.40%) (5.76%) (2.03%) (100%)

[100.00%] [100.00%] [100.00%] [100.00%] [100.00%]

Panel B: Percentage of the number of orders submitted by trader types in the regular trading period

MO (0.39%) (94.03%) (1.56%) (4.01%) 4,094,013 (100%)

[0.00%] [4.59%] [0.16%] [0.70%] [0.52%]

BB1Q (73.06%) (19.60%) (5.37%) (1.98%) 102,083,246 (100%)

[11.74%] [23.86%] [13.73%] [8.60%] [13.05%]

B1Q (84.73%) (9.98%) (4.17%) (1.12%) 265,297,478 (100%)

[35.39%] [31.57%] [27.71%] [12.68%] [33.91%]

B2-5Q (86.54%) (6.16%) (6.50%) (0.80%) 323,848,232 (100%)

[44.13%] [23.77%] [52.79%] [11.05%] [41.39%]

BB5Q (63.73%) (15.61%) (2.57%) (18.09%) 87,076,897 (100%)

[8.74%] [16.21%] [5.60%] [66.98%] [11.13%]

TOSN

635,128,841 83,847,644 39,898,425 23,524,956 782,399,866

(81.18%) (10.72%) (5.10%) (3.01%) (100%)

[100%] [100%] [100%] [100%] [100%]

TOSF

35,169,413 16,985,537 3,165,669 2,422,677 57,743,296

(60.91%) (29.42%) (5.48%) (4.20%) (100%)

[100%] [100%] [100%] [100%] [100%]

Notes: The table presents order book statistics of call options by trader types from January 1, 2007 to December

31, 2008. Panel A and Panel B show the percentages of the number of submitted orders by market makers (MM),

individual traders (IT), foreign institutional traders (FIT), and domestic institutional traders (DIT) in the pre-open

period and in the regular trading period, respectively. All the order books are divided into the following categories

based on quotes: MO (market order); BB1Q (better best 1 quote), which is submitted limit orders to the better best

quote; B1Q (best 1 quote), which is the limit orders at the best 1 quote; B2-5Q (best 2–5 quotes), which refers to

limit orders that are submitted to behind the best 1 quote but at or before the best 5 quotes; and BB5Q (behind

best 5 quotes), which is submitted limit orders behind the best 5 quotes. In addition, we also report the total number

of submitted orders (TOSN) and total frequency of order submission (TOSF) by each trade type. In each row, the

numbers in parentheses represent the percentages of orders in each order type submitted by MM, IT, FIT, and

DIT, respectively. The numbers in brackets for each column are the percentages of order types by each trader type

himself.

44

Table 2: Order book statistics of put options by trader type categories

MM IT FIT DIT TOSN

Panel A: Percentage of the number of orders submitted by trader types in the pre-open period

MO (0.65%) (95.96%) (0.50%) (2.90%) 36,815 (100%)

[0.02%] [0.74%] [0.03%] [0.53%] [0.53%]

Limit Order (19.75%) (68.59%) (8.75%) (2.91%) 6,911,285 (100%)

[99.98%] [99.26%] [99.97%] [99.47%] [99.47%]

TOSN

1,365,235 4,775,800 605,198 201,867 6,948,100

(19.65%) (68.74%) (8.71%) (2.91%) (100%)

[100%] [100%] [100%] [100%] [100%]

Panel B: Percentage of the number of orders submitted by trader types in the regular trading period

MO (1.10%) (93.42%) (0.94%) (4.53%) 2,950,423 (100%)

[0.00%] [4.71%] [0.07%] [0.36%] [0.37%]

BB1Q (77.32%) (14.58%) (5.36%) (2.74%)

102,876,554

(100%)

[11.90%] [25.62%] [14.88%] [7.56%] [12.84%]

B1Q (88.05%) (7.00%) (3.77%) (1.18%)

281,017,358

(100%)

[37.03%] [33.60%] [28.58%] [8.91%] [35.08%]

B2-5Q (86.95%) (3.90%) (5.86%) (3.29%)

324,663,582

(100%)

[42.24%] [21.62%] [51.37%] [28.64%] [40.52%]

BB5Q (65.74%) (9.44%) (2.11%) (22.71%) 89,647,125 (100%)

[8.82%] [14.46%] [5.10%] [54.54%] [11.19%]

TOSN

668,230,419 58,548,238 37,044,280 37,332,105 801,155,042

(83.41%) (7.31%) (4.62%) (4.66%) (100%)

[100%] [100%] [100%] [100%] [100%]

TOSF

39,356,130 12,586,341 2,962,968 3,262,635 58,168,074

(67.66%) (21.64%) (5.09%) (5.61%) (100%)

[100%] [100%] [100%] [100%] [100%]

Notes: The table presents order book statistics of put options by trader types from January 1, 2007 to December

31, 2008. Panel A and Panel B show the percentages of the number of submitted orders by market makers (MM),

individual traders (IT), foreign institutional traders (FIT), and domestic institutional traders (DIT) in the pre-open

period and in the regular trading period, respectively. All the order books are divided into the following categories

based on quotes: MO (market order); BB1Q (better best 1 quote), which is submitted limit orders to the better best

quote; B1Q (best 1 quote), which is the limit orders at the best 1 quote; B2-5Q (best 2–5 quotes), which refers to

limit orders that are submitted to behind the best 1 quote but at or before the best 5 quotes; and BB5Q (behind

best 5 quotes), which is submitted limit orders behind the best 5 quotes. In addition, we also report the total number

of submitted orders (TOSN) and total frequency of order submission (TOSF) by each trade type. In each row, the

numbers in parentheses represent the percentages of orders in each order type submitted by MM, IT, FIT, and

DIT, respectively. The numbers in brackets for each column are the percentages of order types by each trader type

himself.

45

Table 3: Arbitrage profits

All sample In-the-money (ITM)

(myn <0.975)

At-the-money (ATM)

(0.975 <= myn <=1.025)

Out-the-money (OTM)

(myn >1.025)

Obs. 27805 15318 10917 1570

Mean 3.5244 3.3920 3.4083 5.6227

Std 4.6958 3.7078 4.3851 10.8672

Median 2.6321 2.7848 2.5971 2.7949

Min 0.0002 0.0002 0.0025 0.0003

Max 178.5411 123.6421 160.4133 178.5411

Skewness 13.6965 11.1457 16.0534 7.4167

Kurtosis 332.7765 268.6778 450.7541 81.5309

Notes: The table reports the statistics of arbitrage profits as violating the put-call futures parity (PCFP). The data

cover the period from January 1, 2007 to December 31, 2008. The total costs for building the arbitrage portfolio

consist of trade costs and opportunity costs of margin deposits. The transaction costs include the pairs of call and

put options and a futures contract. We further separate the options violating the PCFP into three groups by call

option’s moneyness: for in-the-money options, at-the-money options, and out-the-money options. The option

moneyness (myn) is calculated as K/(S*erτ), in which K is exercise price, S is the underlying asset price, τ is time

to maturity, and r is risk-free interest rate.

46

Table 4 Submitted orders after violating the put-call futures parity

Panel A: In a 15-second time interval just after violating the put-call futures parity

Overvalued call Overvalued put

Bid orders Ask orders Ratio Bid orders Ask orders Ratio

Vol. Cum.

(A) Vol.

Cum.

(B) =(A/B) Vol.

Cum.

(A) Vol.

Cum.

(B) =(A/B)

MO 0.49 0.49 0.81 0.81 0.60 MO 0.35 0.35 0.45 0.45 0.78

BB1Q 5.85 6.34 7.89 8.71 0.73 BB1Q 5.98 6.34 36.17 36.62 0.17

B1Q 8.11 14.45 8.31 17.02 0.85 B1Q 7.69 14.03 11.24 47.86 0.29

B2-5Q 9.78 24.24 8.22 25.24 0.96 B2-5Q 23.77 37.80 17.18 65.04 0.58

BB5Q 5.68 29.91 2.73 27.98 1.07 BB5Q 21.25 59.06 7.29 72.33 0.82

Undervalued call Undervalued put


Vol. Cum.

(A) Vol.

Cum.

(B) =(A/B) Vol.

Cum.

(A) Vol.

Cum.

(B) =(A/B)

MO 0.66 0.66 0.32 0.32 2.04 MO 0.45 0.45 0.50 0.50 0.90

BB1Q 38.40 39.06 7.16 7.48 5.22 BB1Q 6.49 6.93 5.49 5.99 1.16

B1Q 13.26 52.32 8.02 15.50 3.38 B1Q 8.23 15.16 6.26 12.24 1.24

B2-5Q 21.01 73.33 25.15 40.65 1.80 B2-5Q 6.51 21.67 4.22 16.47 1.32

BB5Q 7.22 80.55 19.71 60.36 1.33 BB5Q 2.33 24.00 2.44 18.90 1.27

Panel B: In a 30-second time interval just after violating the put-call futures parity

Overvalued call Overvalued put


Vol. Cum.

(A) Vol.

Cum.

(B) =(A/B) Vol.

Cum.

(A) Vol.

Cum.

(B) =(A/B)

MO 0.98 0.98 1.60 1.60 0.61 MO 1.19 1.19 0.87 0.87 1.37

BB1Q 11.65 12.63 15.12 16.72 0.76 BB1Q 12.44 13.62 62.41 63.27 0.22

B1Q 16.69 29.31 16.25 32.97 0.89 B1Q 16.27 29.89 21.01 84.28 0.35

B2-5Q 20.16 49.47 15.87 48.84 1.01 B2-5Q 47.69 77.58 32.13 116.41 0.67

BB5Q 11.01 60.49 5.39 54.23 1.12 BB5Q 38.43 116.02 13.69 130.10 0.89

Undervalued call Undervalued put


Vol. Cum.

(A) Vol.

Cum.

(B) =(A/B) Vol.

Cum.

(A) Vol.

Cum.

(B) =(A/B)

MO 1.23 1.23 0.69 0.69 1.80 MO 0.88 0.88 0.97 0.97 0.91

BB1Q 65.58 66.81 14.76 15.45 4.33 BB1Q 12.25 13.12 10.97 11.94 1.10

B1Q 25.27 92.08 17.99 33.44 2.75 B1Q 15.68 28.81 12.78 24.73 1.16

B2-5Q 38.50 130.58 49.95 83.38 1.57 B2-5Q 12.28 41.08 8.53 33.26 1.24

BB5Q 13.75 144.33 35.37 118.75 1.22 BB5Q 4.56 45.64 4.52 37.78 1.21

Notes: The table presents the ratios of the cumulative average number of submitted bid orders to ask orders by

quote types in the initial arbitrage shocks. The results in first 15-second and 30-second time intervals of arbitrage

shocks are reported in Panel A and Panel B, respectively. The quoted orders are divided into the following

categories: MO (market order), BB1Q (better best quote), B1Q (best 1 quote), B2-5Q (best 2–5 quotes), and BB5Q

(behind best 5 quotes). They are arranged in highly executed probability order. For each type of arbitrage

opportunities (with 24976 observations for overvalued calls and undervalued puts, and with 2827 observations

for undervalued calls and overvalued puts), we compute the ratio of submitted bid orders to ask orders (A/B) by

each quote type. The ratios for quote types are calculated as the cumulative average number of submitted bid

orders (A) to the cumulative average number of submitted ask orders (B). Vol. denotes the average number of

submitted orders in all violations. Cum. (A) is the cumulative average number of submitted orders by quote types.

47

Table 5 Change ratios of order submission before and after violating PCFP

Panel A: In two 15-second time intervals before and after violating the put-call futures parity

Overvalued call: On bid side Overvalued put: On bid side

MM IT FIT DIT TOSN MM IT FIT DIT TOSN

MO 0.00% -0.05% 0.00% -0.02% -0.08% MO 0.00% -0.23% 0.00% 0.04% -0.19%

BB1Q 1.40% 0.32% 0.03% -0.03% 1.73% BB1Q 4.03% 0.48% 0.30% 0.16% 4.97%

B1Q 1.52% -0.97% -0.01% -0.06% 0.48% B1Q 10.97% -1.30% 0.07% 0.11% 9.85%

B2-5Q 0.57% -1.59% -0.21% -0.08% -1.30% B2-5Q 7.75% -2.47% 0.13% 0.12% 5.53%

BB5Q -0.54% -1.69% -0.24% -0.11% -2.59% BB5Q 1.10% -2.55% -0.30% -0.20% -1.94%

Undervalued call: On ask side Undervalued put: On ask side


MO 0.00% 0.05% 0.00% 0.04% 0.09% MO 0.00% -0.04% 0.00% 0.00% -0.04%

BB1Q 3.38% 0.41% 0.18% 0.17% 4.14% BB1Q 1.50% 0.17% 0.00% -0.06% 1.62%

B1Q 10.14% -0.04% -0.18% 0.12% 10.04% B1Q 2.45% -1.06% -0.25% -0.21% 0.92%

B2-5Q 8.34% -0.42% -0.28% 0.25% 7.89% B2-5Q 1.07% -1.39% -0.39% -0.26% -0.98%

BB5Q 2.29% -0.12% -0.59% 0.03% 1.60% BB5Q 0.09% -1.59% -0.36% -0.34% -2.20%

Panel B: In two 30-second time intervals before and after violating the put-call futures parity

Overvalued call: On bid side Overvalued put: On bid side


MO 0.00% -0.07% 0.00% -0.03% -0.10% MO 0.00% -0.14% 0.00% 0.04% -0.09%

BB1Q 0.87% 0.00% -0.01% -0.04% 0.82% BB1Q 3.58% 0.24% 0.13% 0.15% 4.10%

B1Q 1.29% -0.99% 0.00% -0.06% 0.24% B1Q 10.05% -0.67% 0.01% 0.15% 9.55%

B2-5Q 0.84% -1.38% -0.14% -0.09% -0.76% B2-5Q 7.26% -1.13% -0.15% -0.01% 5.97%

BB5Q -0.20% -1.54% -0.17% -0.09% -2.01% BB5Q 2.54% -1.11% -0.36% -0.40% 0.67%

Undervalued call: On ask side Undervalued put: On ask side


MO 0.00% 0.06% 0.00% 0.01% 0.07% MO 0.00% -0.10% 0.00% -0.01% -0.11%

BB1Q 3.78% 0.32% 0.24% 0.08% 4.42% BB1Q 1.02% -0.13% 0.06% -0.07% 0.88%

B1Q 10.82% 0.42% 0.26% -0.06% 11.44% B1Q 2.25% -1.01% -0.10% -0.25% 0.90%

B2-5Q 9.43% 0.12% 0.30% 0.00% 9.86% B2-5Q 1.23% -1.30% -0.18% -0.24% -0.49%

BB5Q 5.11% 0.20% 0.13% -0.26% 5.18% BB5Q 0.15% -1.44% -0.16% -0.23% -1.67%

Notes: The table presents the change ratios of submitted orders accumulated by quote types during times of before

and after violating PCFP. Panel A and Panel B report the results in two 15-second time intervals and two 30-

second time intervals just before and after PCFP violations, respectively. For each type of PCFP violations and

each trader type, we compute the ratios of change in number of submitted orders accumulated by quote types. The

ratios for quote types are calculated as the differences between average numbers of submitted orders accumulated

by quote types to average number of all submitted orders at prior time interval. More specifically, we first calculate

the differences between cumulative numbers of submitted orders by quote types in two 15-second (or 30-second)

time intervals of just before and after violating PCFP and average them. Then, they are divided by the average

number of all submitted orders in 15-second (or 30-second) time interval of just before violating PCFP. In addition,

the quoted orders are selected on the opposite trade direction of arbitrageurs and divided into the following

categories: MO (market order), BB1Q (better best quote), B1Q (best 1 quote), B2-5Q (best 2–5 quotes), and BB5Q

(behind best 5 quotes). The order types are arranged in highly executed probability order.

48

Table 6 Regression results of liquidity provision by trader types for overvalued calls

All MM IT FIT DIT

Fixed effect Fixed effect Fixed effect Fixed effect Fixed effect

Stat. t-value Stat. t-value Stat. t-value Stat. t-value Stat. t-value

NBPt-1 0.11 51.58*** 0.04 23.53*** 0.06 59.37*** 0.00 4.64*** 0.00 29.28***

RVt-1 209.07 34.28*** 187.92 40.07*** -2.22 -0.72 19.27 10.85*** 4.11 9.36***

ArbSzt-1 -0.46 -24.80*** -0.28 -19.79*** -0.08 -8.62*** -0.09 -16.40*** -0.01 -6.27***

FRett-1 210.16 71.89*** 126.65 56.33*** 54.63 36.95*** 27.74 32.59*** 1.13 5.35***

OVolt-1 16.10 83.61*** 10.28 69.42*** 4.47 45.87*** 0.97 17.35*** 0.38 27.37***

OSpdt-1 -0.23 -16.53*** -0.15 -14.05*** -0.03 -3.88*** -0.05 -12.81*** 0.00 -0.47

TolBidt-1 -3.37 -32.63*** -1.27 -16.00*** -1.57 -30.07*** -0.55 -18.32*** 0.02 2.97***

TolAskt-1 -0.10 -1.03 0.81 10.61*** -1.10 -21.87*** 0.19 6.40*** 0.00 0.19

Mynt -473.22 -5.14*** -260.12 -3.67*** -154.56 -3.32*** -78.45 -2.93*** 19.91 3.00***

D1 0.27 0.90 0.47 2.06** -0.22 -1.44 0.01 0.15 0.00 -0.08

D2 -0.35 -1.19 0.06 0.25 -0.34 -2.28** -0.05 -0.59 -0.02 -0.82

D3 -0.37 -1.24 -0.03 -0.13 -0.32 -2.17** 0.00 -0.04 -0.01 -0.43

D4 -0.50 -1.69* -0.07 -0.31 -0.45 -2.99*** 0.04 0.48 -0.02 -1.05

D5 -0.41 -1.39 0.00 0.01 -0.42 -2.79*** 0.01 0.17 -0.01 -0.55

D6 -0.41 -1.39 -0.07 -0.30 -0.42 -2.80*** 0.08 0.90 0.00 -0.06

D7 -0.38 -1.30 0.10 0.45 -0.50 -3.32*** 0.02 0.22 -0.01 -0.41

D8 -0.42 -1.44 -0.02 -0.08 -0.44 -2.93*** 0.05 0.55 -0.02 -0.74

D9 -0.28 -0.95 0.02 0.08 -0.38 -2.54** 0.08 0.88 0.00 0.21

D10 -0.48 -1.63 -0.17 -0.73 -0.37 -2.45** 0.07 0.80 -0.02 -0.90

D11 -0.26 -0.90 0.13 0.59 -0.39 -2.61*** -0.02 -0.18 0.01 0.30

D12 -0.34 -1.14 -0.05 -0.20 -0.33 -2.23** 0.04 0.42 0.01 0.27

0.33 3.86*** -0.03 -0.49 0.38 8.83*** -0.03 -1.09 0.01 1.23

Adj-R2 — 3.32% — 2.04% — 1.57% — 0.41% — 0.34%

Notes: The table presents the unbalanced panel regression results of liquidity supply on buy side by trade types

for overvalued calls after violating PCFP. The second row reports the results of Hausman test (1978) for different

trader types. The results indicate which the fixed effect model or the random effect model is suitable for these panel

data. The empirical model is specified as

, 1 , 1 2 1 3 , 1 4 1 5 , 1

12

6 , 1 7 , 1 8 , 1 9 , ,

1

* * * * *

* * * * *

i t i t t i t t i t

i t i t i t i t j j t t

j



i = 1,2,3,...,N,t = -a,...,0,...,b,a,b [3,12]

(3)

The dependent variable, tNLM , denotes the number of submitted buy orders during t time interval. N is the number of

violating PCFP. The time interval t=0 indicates the occurrence of arbitrage opportunity. j,tD is a dummy variable that

equals 1 if it is in jth interval, j=1,2,3,…, 12. This dummy variable captures the intraday variation in the number of

submitted bid orders with respect to the time of violating the PCFP. For control variables, 1tNBP is option net buy

pressure during t-1 time interval, which is measured in terms of its persistence on buy side. 1tRV is the realized volatility

of futures during t-1 time interval, which controls the impact of volatility on order placement. 1tArbSz is the profit for

arbitrage trade at time t-1. 1tOVol and 1tOSpd denote option trade volume and its average best bid-ask spread during t-

1 time interval, which control for the effect of option volume and spread on order placements. 1tTolBid and 1tTolAsk

are the average of option bid and ask volume at the best 5 quotes during the t-1 time interval, respectively. 1tFRet is the

futures return during t-1 time period. tMyn is option moneyness at time t. In addition, both coefficients of TolBiid and

TolAsk are multiplied by 100 and the coefficient of FRet is divided by 100. ***, **, and * indicate that the t-

values are significant at the 0.01, 0.05, and 0.1, respectively.

49

Table 7 Regression results of liquidity provision by trader types for overvalued puts

All MM IT FIT DIT



NBPt-1 0.16 14.81*** 0.00 0.18 0.15 33.05*** 0.00 1.72* 0.00 3.23***

RVt-1 124.44 18.56*** 121.38 22.01*** -10.50 -3.73*** 3.59 2.54** 9.97 11.48***

ArbSzt-1 -0.12 -4.34*** -0.08 -3.53*** -0.03 -2.65*** 0.00 -0.34 -0.01 -1.96**

FRett-1 25.85 7.28*** 30.75 10.53*** -3.34 -2.24** -2.65 -3.53*** 1.09 2.36**

OVolt-1 19.47 18.52*** 5.87 6.78*** 12.90 29.22*** 0.34 1.54 0.36 2.67***

OSpdt-1 -0.06 -3.81*** -0.05 -3.57*** -0.01 -1.21 -0.01 -1.55 0.00 -0.27

TolBidt-1 -1.49 -3.26*** -0.98 -2.62*** -0.17 -0.86 -0.35 -3.62*** 0.01 0.13

TolAskt-1 0.62 0.93 1.32 2.41** -0.89 -3.19*** 0.06 0.41 0.14 1.61

Mynt 163.23 0.96 99.34 0.71 2.78 0.04 10.68 0.30 50.44 2.29**

D1 5.23 4.59*** 5.42 5.79*** -0.42 -0.88 0.27 1.13 -0.05 -0.32

D2 3.21 2.92*** 2.60 2.88*** 0.86 1.86* -0.05 -0.23 -0.20 -1.39

D3 -0.59 -0.54 0.31 0.34 -0.15 -0.33 -0.42 -1.84* -0.32 -2.25**

D4 -2.08 -1.91* -1.47 -1.64 -0.63 -1.38 0.13 0.58 -0.12 -0.82

D5 -1.84 -1.69* -1.27 -1.42 0.05 0.11 -0.30 -1.30 -0.33 -2.32**

D6 -0.36 -0.33 -0.32 -0.35 -0.03 -0.07 0.16 0.68 -0.16 -1.15

D7 -0.80 -0.73 -0.34 -0.38 -0.26 -0.56 -0.06 -0.27 -0.14 -0.98

D8 -1.63 -1.50 -0.92 -1.03 -0.62 -1.35 0.14 0.60 -0.23 -1.61

D9 -1.40 -1.28 -0.67 -0.75 -0.71 -1.55 0.10 0.44 -0.11 -0.80

D10 -1.82 -1.67* -0.75 -0.84 -1.13 -2.46** 0.23 1.00 -0.17 -1.20

D11 -2.11 -1.93* -1.06 -1.18 -1.05 -2.28** 0.32 1.40 -0.33 -2.31**

D12 -3.98 -3.63*** -2.73 -3.03*** -0.97 -2.11** -0.06 -0.25 -0.22 -1.58

0.69 2.18** 0.10 0.39 0.43 3.22*** -0.04 -0.58 0.20 4.89***

Adj-R2 — 1.50% — 1.26% — 2.41% — 0.05% — 0.28%

Notes: The table presents the unbalanced panel regression results of liquidity supply on buy side by trade types

for overvalued puts after violating PCFP. The second row reports the results of Hausman test (1978) for different



, 1 , 1 2 1 3 , 1 4 1 5 , 1

12

6 , 1 7 , 1 8 , 1 9 , ,

1

* * * * *

* * * * *

i t i t t i t t i t


j



i = 1,2,3,...,N,t = -a,...,0,...,b,a,b [3,12]

(3)





pressure during t-1 time interval. 1tRV is the realized volatility of futures during t-1 time interval. 1tArbSz is the profit

for arbitrage trade at time t-1. 1tOVol and 1tOSpd denote option trade volume and its average best bid-ask spread during

t-1 time interval. 1tTolBid and 1tTolAsk are the average of option bid and ask volume at the best 5 quotes during the t-

1 time interval, respectively. 1tFRet is the futures return during t-1 time period. tMyn is option moneyness at time t. In

addition, both coefficients of TolBiid and TolAsk are multiplied by 100 and the coefficient of FRet is divided by

100. ***, **, and * indicate that the t-values are significant at the 0.01, 0.05, and 0.1, respectively.

50

Table 8 Regression results of liquidity provision by trader types for undervalued calls

All MM IT FIT DIT

Fixed effect Random effect Fixed effect Fixed effect Random effect


NBPt-1 -0.06 -4.98*** -0.06 -4.92*** 0.00 -0.22 -0.01 -2.99*** 0.00 -3.18***

RVt-1 195.25 25.56*** 173.10 25.14*** 10.18 3.99*** 6.41 5.28*** 8.63 11.07***

ArbSzt-1 -0.32 -10.69*** -0.10 -3.81*** -0.16 -15.40*** 0.00 -0.48 -0.01 -3.77***

FRett-1 19.98 4.95*** 23.81 6.48*** -4.54 -3.36*** -2.83 -4.40*** 3.74 9.01***

OVolt-1 10.33 8.65*** 8.33 7.76*** 0.65 1.63 1.07 5.64*** -0.12 -0.97

OSpdt-1 -0.05 -1.21 -0.13 -3.90*** -0.03 -2.68*** -0.01 -1.28 0.00 -0.14

TolBidt-1 -2.75 -4.23*** -0.57 -1.14 0.16 0.76 -0.04 -0.36 -0.04 -0.59

TolAskt-1 -1.74 -2.68*** 1.44 2.80*** -0.12 -0.55 -0.27 -2.66*** 0.06 1.06

Mynt -301.78 -1.56 -114.37 -9.21*** -242.70 -3.75*** 23.02 0.75 -11.32 -6.68***

D1 7.28 5.63*** 5.65 4.62*** 1.01 2.33** -0.16 -0.76 -0.22 -1.59

D2 2.96 2.38*** 3.01 2.55*** 0.00 0.00 0.03 0.14 -0.46 -3.42***

D3 -0.99 -0.80 -0.32 -0.27 -0.18 -0.43 -0.12 -0.60 -0.53 -4.00***

D4 -1.05 -0.85 -0.55 -0.47 0.19 0.46 -0.36 -1.82* -0.40 -3.05***

D5 -1.06 -0.86 -0.51 -0.43 -0.24 -0.57 0.15 0.77 -0.49 -3.68***

D6 -1.16 -0.94 -1.22 -1.04 0.36 0.87 0.20 1.03 -0.50 -3.77***

D7 -2.69 -2.17** -2.40 -2.04** 0.25 0.59 -0.20 -1.02 -0.36 -2.73***

D8 -3.06 -2.47** -1.72 -1.46 -0.68 -1.64 -0.12 -0.58 -0.57 -4.27***

D9 -0.34 -0.27 0.56 0.48 -0.72 -1.75* 0.30 1.50 -0.51 -3.82***

D10 -1.19 -0.96 -0.24 -0.21 -0.50 -1.22 0.03 0.18 -0.51 -3.87***

D11 -0.79 -0.64 0.53 0.45 -0.69 -1.67* -0.17 -0.88 -0.48 -3.63***

D12 -3.29 -2.64*** -2.11 -1.79* -0.63 -1.51 -0.16 -0.79 -0.38 -2.89***

0.45 1.26 150.53 11.86*** 0.16 1.29 0.05 0.84 14.40 8.28***

Adj-R2 — 1.57% — 1.50% — 0.51% — 0.14% — 0.54%

Notes: The table presents the unbalanced panel regression results of liquidity supply on sell side by trade types

for undervalued calls after violating PCFP. The second row reports the results of Hausman test (1978) for different



, 1 , 1 2 1 3 , 1 4 1 5 , 1

12

6 , 1 7 , 1 8 , 1 9 , ,

1

* * * * *

* * * * *

i t i t t i t t i t


j



i = 1,2,3,...,N,t = -a,...,0,...,b,a,b [3,12]

(3)











51

Table 9 Regression results of liquidity provision by trader types for undervalued puts

All MM IT FIT DIT



NBPt-1 -0.06 -33.91*** -0.03 -22.32*** -0.03 -35.92*** 0.01 21.20*** 0.00 -14.59***

RVt-1 128.59 25.37*** 92.71 22.16*** 30.91 12.54*** -2.16 -2.17** 7.12 9.43***

ArbSzt-1 -0.12 -9.63*** -0.08 -7.44*** -0.04 -6.17*** -0.01 -3.17*** 0.00 0.92

FRett-1 73.34 30.40*** 46.48 23.34*** 25.76 21.96*** 0.04 0.07 1.06 2.94***

OVolt-1 19.83 125.01*** 14.53 110.92*** 4.52 58.61*** 0.45 14.44*** 0.33 14.04***

OSpdt-1 -0.11 -4.56*** -0.12 -5.89*** 0.00 0.13 0.00 -0.80 0.01 2.66***

TolBidt-1 -0.03 -0.50 -0.01 -0.12 -0.04 -1.24 -0.06 -5.05*** 0.07 8.00***

TolAskt-1 0.08 2.87*** 0.11 4.59*** -0.02 -1.14 -0.01 -2.26** 0.00 0.53

Mynt 219.99 2.87*** 485.76 7.67*** -206.29 -5.53*** 97.29 6.46*** -156.76 -13.72***

D1 0.25 1.00 0.41 2.01** -0.12 -0.98 -0.04 -0.74 -0.01 -0.27

D2 -0.16 -0.65 0.05 0.25 -0.18 -1.51 -0.01 -0.22 -0.02 -0.53

D3 -0.43 -1.73* -0.16 -0.80 -0.20 -1.67* -0.03 -0.66 -0.03 -0.90

D4 -0.24 -0.97 -0.06 -0.29 -0.18 -1.50 0.04 0.88 -0.04 -1.17

D5 -0.34 -1.40 -0.15 -0.73 -0.15 -1.23 0.00 -0.01 -0.05 -1.36

D6 -0.37 -1.51 -0.20 -0.99 -0.09 -0.77 -0.07 -1.41 -0.01 -0.27

D7 -0.14 -0.59 0.05 0.25 -0.17 -1.44 -0.01 -0.13 -0.02 -0.45

D8 -0.46 -1.87* -0.21 -1.03 -0.13 -1.08 -0.05 -1.04 -0.07 -1.95*

D9 -0.45 -1.85* -0.19 -0.93 -0.17 -1.43 -0.06 -1.15 -0.04 -1.05

D10 -0.32 -1.30 -0.08 -0.40 -0.17 -1.46 -0.03 -0.66 -0.03 -0.85

D11 -0.32 -1.30 -0.01 -0.04 -0.23 -1.91* -0.05 -0.94 -0.04 -1.01

D12 -0.09 -0.35 0.10 0.51 -0.19 -1.57 -0.02 -0.38 0.02 0.44

0.26 3.61*** 0.04 0.63 0.16 4.78*** 0.03 1.87* 0.03 2.71***

Adj-R2 — 3.37% — 2.53% — 1.06% — 0.11% — 0.14%

Notes: The table presents the unbalanced panel regression results of liquidity supply on sell side by trade types

for undervalued puts after violating PCFP. The second row reports the results of Hausman test (1978) for different



, 1 , 1 2 1 3 , 1 4 1 5 , 1

12

6 , 1 7 , 1 8 , 1 9 , ,

1

* * * * *

* * * * *

i t i t t i t t i t


j



i = 1,2,3,...,N,t = -a,...,0,...,b,a,b [3,12]

(3)











52

Table 10 Regression results of limit orders on liquidity

All MM IT FIT DIT


Panel A: Overvalued calls

NLOt 0.02 3.68*** 0.10 5.44*** 0.00 1.56 -0.94 -8.76*** -1.85 -5.73***

DM,t*NLOt 0.03 5.79*** 0.09 5.94*** -0.06 -4.79*** 1.33 6.22*** 11.52 6.00***

Panel B: Overvalued puts

NLOt -0.03 -4.04*** -0.09 -4.15*** -0.12 -5.02*** 1.34 5.85*** -0.10 -2.07**

DM,t*NLOt 0.16 6.23*** 0.16 4.68*** -3.36 -7.54*** -2.11 -5.77*** 1.04 5.02***

Panel C: Undervalued calls

NLOt -0.02 -6.18*** -0.03 -1.99** -0.02 -3.10*** 0.09 0.47 0.20 1.64

DM,t*NLOt 0.11 6.04*** 0.07 2.70*** 0.43 2.89*** -0.13 -0.41 -0.67 -1.24

Panel D: Undervalued puts

NLOt -0.01 -4.10 -0.05 -10.33*** 0.05 6.28*** -0.48 -2.44*** -1.96 -2.45***

DM,t*NLOt 0.08 8.26 *** 0.12 8.62*** 0.60 7.91*** 1.99 5.12*** 4.53 2.63***

Notes: The table presents the unbalanced panel regression results of limit orders on liquidity by each trader type

around PCFP violations. We estimate the coefficients in Equation (4) using the two stages least square (2SLS)

panel regression. The lagged values of number of submitted limit orders (NLO), trade volume (OVol), realized

volatility (RV), net buy pressure (NBP), arbitrage size (ArbSz), and futures return (FRet) are used as instrument

variables. The results for overvalued calls, overvalued puts, undervalued calls, and undervalued puts are reported

in Panels A-D, respectively. In addition, the Hausman test (1978) is used to judge which the fixed effect model or the

random effect model is suitable for the panel data. The empirical model is specified as

, 1 , 2 , 3 , 4 , 1* * * * *i t i t M,t i t i t i t tLiq NLO D NLO OVol Liq

i = 1,2,3,...,N, t = -a,...,0,...,b, and a,b [3,12]

(4)

The dependent variable, tLiq , is the liquidity of option at the end of time interval t, which is measured as bid-ask

spread divided by the midpoint of quote. N is the number of violating PCFP. The time interval t=0 indicates the

occurrence of violating PCFP. The limit orders (NLOt) are calculated as the number of submitted bid and ask orders

available at under better best quote during time t interval (i.e., the sum of bid and ask orders in quote types of

B1Q, 2-5Q, and BB5Q). M,tD is a dummy variable that equals 1 if it is during the period of after violating PCFP. tOVol

is option trade volume during t time interval. t -1Liq is lagged liquidity. In addition, for brevity, we only report the

coefficients of NLO and DM,t*NLO. Both the coefficients are multiplied by 1000. ***, **, and * indicate that the

t-values are significant at the 0.01, 0.05, and 0.1, respectively.

53

Table 11 Active liquidity provision for mispricing calls and puts

All MM IT FIT DIT


Panel A: Overvalued calls

D1 0.09 0.72 0.13 1.38 -0.03 -0.49 0.00 0.02 -0.01 -0.52

D2 -0.15 -1.20 -0.06 -0.69 -0.07 -1.06 0.00 -0.14 -0.01 -0.71

D3 -0.10 -0.79 0.02 0.23 -0.13 -1.92* 0.02 0.50 -0.01 -0.58

D4 -0.11 -0.91 0.02 0.25 -0.13 -2.00** 0.01 0.23 -0.01 -0.65

D5 -0.06 -0.51 0.07 0.74 -0.10 -1.47 -0.03 -0.96 0.00 0.44

D6 -0.01 -0.07 0.07 0.72 -0.08 -1.17 0.01 0.32 -0.01 -0.66

D7 0.15 1.23 0.19 2.14** -0.06 -0.90 0.02 0.60 0.00 -0.41

D8 0.17 1.36 0.21 2.28** -0.05 -0.70 0.01 0.19 0.00 0.04

D9 0.07 0.60 0.12 1.32 -0.05 -0.77 0.01 0.19 0.00 -0.15

D10 0.09 0.71 0.07 0.76 -0.02 -0.32 0.04 1.13 0.00 -0.08

D11 0.05 0.39 0.10 1.11 -0.08 -1.13 0.02 0.67 0.00 0.00

D12 0.11 0.89 0.06 0.63 0.01 0.17 0.04 1.26 0.00 -0.45

Panel B: Overvalued puts

D1 1.18 2.80*** 1.11 3.51*** 0.03 0.12 0.02 0.22 0.06 1.10

D2 1.78 4.39*** 0.74 2.41** 0.96 3.70** 0.00 0.03 0.06 1.18

D3 0.14 0.35 0.06 0.21 0.18 0.71 -0.10 -1.13 -0.01 -0.24

D4 -0.28 -0.70 -0.32 -1.06 0.11 0.41 -0.05 -0.58 0.01 0.23

D5 -0.66 -1.65* -0.30 -0.98 -0.15 -0.59 -0.11 -1.28 -0.05 -1.06

D6 0.37 0.91 0.52 1.71* -0.10 -0.39 0.03 0.35 -0.02 -0.41

D7 -0.23 -0.58 -0.42 -1.38 0.25 0.98 0.02 0.21 -0.05 -1.10

D8 -0.23 -0.57 -0.30 -1.00 0.11 0.41 -0.02 -0.25 0.02 0.36

D9 0.60 1.50 0.60 1.97** -0.15 -0.58 0.10 1.10 0.08 1.63

D10 0.45 1.11 0.66 2.18** -0.33 -1.27 0.05 0.62 0.07 1.46

D11 -0.20 -0.50 -0.10 -0.34 -0.13 -0.51 0.14 1.61 -0.09 -1.71*

D12 0.22 0.53 0.38 1.24 -0.07 -0.28 -0.06 -0.70 -0.01 -0.11

Panel C: Undervalued calls

D1 1.60 2.84*** 1.55 2.97*** 0.05 0.31 -0.04 -0.41 0.05 1.20

D2 0.64 1.18 0.52 1.03 0.08 0.52 0.09 0.85 -0.04 -1.21

D3 -0.06 -0.12 0.08 0.16 0.01 0.09 -0.15 -1.54 0.00 -0.13

D4 -0.29 -0.54 -0.11 -0.23 -0.05 -0.32 -0.09 -0.89 -0.04 -1.05

D5 -0.34 -0.63 -0.04 -0.07 -0.36 -2.36** 0.02 0.21 0.03 0.89

D6 0.15 0.28 0.07 0.14 -0.03 -0.18 0.04 0.40 0.07 1.90*

D7 0.33 0.62 0.18 0.37 0.18 1.19 -0.03 -0.27 0.00 -0.05

D8 -0.14 -0.26 0.34 0.67 -0.18 -1.18 -0.28 -2.82*** -0.02 -0.58

D9 0.81 1.49 0.96 1.92* -0.13 -0.88 -0.01 -0.07 -0.02 -0.42

D10 0.71 1.30 0.68 1.36 -0.03 -0.18 0.07 0.67 -0.02 -0.42

D11 1.36 2.51** 1.54 3.08*** -0.20 -1.30 0.00 -0.01 0.01 0.38

D12 1.24 2.29** 0.98 1.95* 0.01 0.04 0.24 2.41** 0.02 0.42

Panel D: Undervalued puts

D1 0.10 0.74 0.08 0.72 0.04 0.56 -0.02 -0.67 -0.01 -0.61

D2 -0.03 -0.23 -0.06 -0.56 0.02 0.34 -0.01 -0.19 -0.01 -0.24

D3 -0.01 -0.10 0.04 0.40 -0.04 -0.55 0.00 0.07 -0.03 -1.31

D4 -0.07 -0.56 0.02 0.17 -0.07 -0.99 -0.01 -0.51 -0.01 -0.69

D5 -0.17 -1.24 -0.04 -0.39 -0.09 -1.23 -0.03 -0.97 -0.02 -0.72

D6 -0.07 -0.52 0.03 0.29 -0.06 -0.77 -0.04 -1.34 -0.01 -0.55

D7 0.01 0.08 0.14 1.74* -0.11 -1.49 -0.02 -0.68 -0.01 -0.37

D8 -0.07 -0.51 0.02 0.17 -0.05 -0.71 -0.01 -0.50 -0.03 -1.31

D9 -0.20 -1.50 -0.06 -0.59 -0.10 -1.32 -0.03 -0.99 -0.02 -0.94

D10 -0.13 -0.95 0.00 0.02 -0.13 -1.75 0.00 -0.02 -0.01 -0.32

D11 -0.10 -0.76 0.08 0.77 -0.15 -1.99** -0.03 -1.12 -0.01 -0.46

D12 -0.03 -0.19 0.06 0.55 -0.08 -1.02 -0.02 -0.67 0.00 0.20

54

Notes: The table presents the unbalanced panel regression results of liquidity actively providing in the opposite

side of arbitrageurs during times of after violating PCFP. We use the number of submitted orders available at over

best quote (i.e., market order, MO, and better best quote, BB1Q) instead of the number of all submitted orders.

These orders are executed rapidly in the marketplace. The results for overvalued calls, overvalued puts,

undervalued calls, and undervalued puts are reported in Panels A-D, respectively. The Hausman test (1978) is used

to judge which the fixed effect model or the random effect model is suitable for the panel data. The empirical model is

specified as

, 1 , 1 2 1 3 , 1 4 1 5 , 1

12

6 , 1 7 , 1 8 , 1 9 , ,

1

* * * * *

* * * * *

i t i t t i t t i t


j



i = 1,2,3,...,N,t = -a,...,0,...,b,a,b [3,12]

(3)

The dependent variable, tNLM , is the number of submitted orders available at over best quote during t time interval.

N is the number of violating PCFP. The time interval t=0 indicates the occurrence of violating PCFP. j,tD is a dummy

variable that equals 1 if it is in jth interval, j=1,2,3,…, 12. This dummy variable captures the intraday variation in the

number of submitted bid orders with respect to the time of violating the PCFP. For control variables, 1tNBP is option

net buying pressure. 1tRV is the realized volatility of futures. 1tArbSz is the profit for arbitrage trade at time t-1.

1tOVol and 1tOSpd denote option trade volume and its average best bid-ask spread during t-1 time interval. 1tTolBid

and 1tTolAsk are the average of option bid and ask volume at the best 5 quotes during the t-1 time interval, respectively.

1tFRet is the futures return during t-1 time period. tMyn is option moneyness at time t. In addition, ***, **, and *

indicate that the t-values are significant at the 0.01, 0.05, and 0.1, respectively.

Put-call futures parity and liquidity provision by trader ......data, we divide traders by types...

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