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Algorithmic Trading: AnAlgorithmic Trading: An
Overview of Applications AndOverview of Applications And
Models.Models.
Ekaterina Kochieva
Gautam Mitra
Cormac Lucas
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Contents
Introduction
Stock exchange mechanism
Models for trade scheduling
Background
Basic models
References
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Introduction
Until recently, most of financial researchfocused on the investment decisions.
There was a missing part of investment cycle execution of investment decisions.
More over, many investment optimizationmodels assume zero execution cost. But in
reality it is not true. Ignoring this fact may lead to significant
mistake in estimating investment returns.
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Stock exchange mechanism
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Overview of stock exchanges
The main stock exchanges in the world include:
America American Stock Exchange
NASDAQ
New York Stock Exchange So Paulo Stock Exchange
Europe Euronext
Frankfurt Stock Exchange
London Stock Exchange Madrid Stock Exchange
Milan Stock Exchange
Zurich Stock Exchange
Stockholm Stock Exchange
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Overview of stock exchanges Australia/Asia/Africa
Australian Stock Exchange
Bombay Stock Exchange
Hong Kong Stock Exchange
Johannesburg Securities Exchange
Korea Stock Exchange
Shanghai Stock Exchange
Taiwan Stock Exchange
Tokyo Stock Exchange
Toronto Stock Exchange
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Listing requirements LSE main market has requirements for a minimum market
capitalization of 700,000, three years of audited financial statements,minimum public float of 25 % and sufficient working capital for at least
12 months from the date of listing
NASDAQ to be listed a company must have issued at least 1.25million shares of stock worth at least $70 million and must have earnedmore than $11 million over the last three years
NYSE a company must have issued at least a million shares of
stock worth $100 million and must have earned more than $10 millionover the last three years
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Participants
Broker an individual or firm which operates between a buyer and a sellerand usually charge a commission. For most products a licence is required.
Dealer an individual or firm which buys and sells for its own account.
Broker/dealer an individual or firm buying and selling for itself and
others. A registration is required. Principal a role of broker/dealer when buying or selling securities for its
own account.
Market maker a brokerage or bank that maintains a firm bid and askprice in a given security by standing ready, willing, and able to buy or sell atpublicly quoted prices (called making a market). These firms display bid and offer
prices for specific numbers of specific securities, and if these prices are met, theywill immediately buy for or sell from their own accounts.
Specialist a stock exchange member who makes a market for certainexchange-traded securities, maintaining an inventory of those securities andstanding ready to buy and sell shares as necessary to maintain an orderly marketfor those shares. Can be an individual, partnership, corporation or group of firms.
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Prototypical trading systems
Call (periodic) auction selling stocks by bid at intervalsthroughout the day. The orders are stored for execution at a singlemarket clearing price.
Continuous auction buyers enter competitive bids andsellers place competitive offers simultaneously. Continuous, since
orders are executed upon arrival.
Dealership market trading occur between principalsbuying and selling to their own accounts. Firm price quotations areavailable prior to order submission.
Auction markets are concentrated and order-driven
Dealership markets are fragmented and quote-driven
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Examples
NYSE opens with a periodic auction market and then
switches to a continuous auction. Same forTokyo Stock
Exchange.
NASDAQandInternational Stock Exchange
(London) are quote-driven systems (continuous dealershipmarket).
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Examples
Euronext Paris the market is segmented into a numberof different groups of stocks based on size and liquidity. Thetrading mechanisms vary depending on the segment.
Euronext 100, Next 150 ,CAC40 indices and stocks which have
more than 2,500 order book transactions per year continuousauction.
Other stocks call auction twice a day.
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Order types
Market order immediate execution at the best priceavailable when the order reaches the marketplace
Limit order to execute a transaction only at a specifiedprice (the limit) or better
Stop order
Good till cancelled
Fill-or-kill All or None
Day order
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Limit order book A register for limit buy orders and a registry for limit
sell orders.
Limit orders are queued for execution againstincoming market orders using price then time priority
rules.
Transparency: how much top orders can be viewed
More transparent order book allows to see what ishappening in the market and make more accurate
forecasts
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Limit order book
0
500
1000
1500
2000
49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5
Bid
Ask
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Cumulative Order Book
0
0.05
0.1
0.15
0.20.25
0.3
0.35
0.4
4,2
00
3,5
00
2,5
00
1,5
00
500
0 500
1,5
00
2,5
00
3,5
00
4,5
00
Size
Avg.
Price($
/Share)
Cum. Bid
Cum. Ask
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Example
Euronext Paris high transparency market:
Brokers observe the full limit book at all times
Other investors can observe the volume of
orders available at the five best prices
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Placing orders: How does it work?
Exchange
Electronic
Communications
Network
Market
MakerFirm Internalizes
Order
Internet
order
Phone
order
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Electronic Communication
Network ECN is a computer system that facilitates trading of financial
products outside of stock exchanges. The primary products that
are traded on ECNs are stocks and currencies.
In order to trade with an ECN, one must be a subscriber. ECN
subscribers can enter limit orders into the ECN, usually via a
custom computer terminal or a direct dial-up. The ECN will post
those orders on the system for other subscribers to view. The
ECN will then match contra-side orders for execution.
Generally, the buyer and seller are anonymous, with the trade
execution reports listing the ECN as the party.
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Principal bid
A transaction where a broker/dealer provide
an investor with guaranteed execution of the
trade list at the market prices at a specificpoint in time.
All timing risk is transferred to broker/dealers.
Investors are charged a premium for this.
Blind bid investor provides only trade list
statistics. Than broker/dealer defines the
price.
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The spread between Principal and
AgencyInvestor Cost
ImplicationsAgency Execution
Principal Bid
Transaction
Trading Costs
Comission Yes NoPrice Appreciation Yes No
Market Impact Yes No
Timing Risk Yes No
Opportunity Cost Yes No
Premium Fee No YesKnown Price No Yes
Guaranteed Completion No Yes
Trading Cost Forecast Distribution ofCost Single Value Estimate
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Models for tradeS
cheduling
1. Background
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Trading cost iceberg
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Potential execution strategies
Min cost in presence of risk
Balance trade off between cost and risk
Max probability of price improvement
*k
k
R)R(xs.t.
)(xMin
e
)R(x)(xMin kk
*
k L))(xProb(Max eN
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Constraints
Completion
Monotony (shrinking portfolio)
Participation rate
Cash balance
i
j
ij Xx !
1e ijij rr
Ee
ijij
ij
vx
x
maxmin DcashD j ee
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Market impact
Market impact is primarily caused by: Supply-demand imbalance (liquidity needs)
Information leakage
Market impact could be
Temporary occurs when the order is released but does
not alter markets long-term outlook caused by liquidity demandand immediacy requirements.
Permanent long-term change in price caused by anorder.
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Market impact bubble
Time
Price
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Temporary market impact
Time
Price
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P
ermanent market impact
Time
Price
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Long-lived Temporary MI
Time
Price
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Timing risk. Opportunity risk. Timing risk grows from the uncertainty
surrounding trading cost estimates. It
includes price volatility and instability involume profiles during a day.
Opportunity risk is of not being able to
implement investment decision in full. It is
caused by insufficient stock liquidity orunfavourable price movement.
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Models for tradeS
cheduling
2. Basic models
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Bertsimas and Lo Fixed blocks of shares s=[s1,,sn]
Fixed finite number of periods T
Set of price dynamics: Price = no-impact price + linear impact function
Find optimal sequence of trade to minimize expected
transaction cost
tttpp H! ~
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Further improvements Almgren and Chriss (2000) permanent and
temporary impact, efficient frontier of execution.
Almgren (2003) non-linear impact function.
Malamut (2002) instantaneous market impact: pre-
calculated aggregate impact value to each period.
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Further improvements
Kissel and Glantz(2003) ETF used to define besttrading strategies. Concept of a capital trade line (CTL) formixed trading strategies (agency versus principal bid).
Obizhaeva and Wang (2005) addingsupply/demand dynamics. Model includes discrete andcontinuous trading.
Engle and Ferstenberg (2006) integration ofportfolio decision and the execution decision. Hedging thetrading risk.
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References
Almgren, R. and N. Chriss, 2000, Optimal Execution of PortfolioTransactions. Journal of Risk 3, 5-39
Almgren, R., 2003, Optimal Execution with Nonlinear Impact
Functions and Trading-enhanced Risk.A
pplied MathematicalFinance 10, 1-18
Bertsimas, D. and A. W. Lo, 1998,Optimal Control of ExecutionCosts. J. Financial Markets 1, 1-50.
Malamut R., 2002, Multi-Period Optimization Techniques fortrade Scheduling, QWAFAFEW presentation
Obizhaeva, A. and J. Wang, 2005,Optimal Trading Strategyand Supply/Demand dynamics, NBER working paper
Engle, R., and R. Ferstenberg, 2006, Execution Risk, NBERworking paper
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References
Kissel, R. and M. Glantz, 2003, Optimal Trading Strategies.
Amacom
Bennouri, M., 2005, Auction versus Dealership Markets
Madhavan, A., 1992, trading Mechanisms in Securities Markets.The Journal of Finance, vol. XLVII, 2
Comerton-Forde,C. and A. Frino, 2004,The Impact of Limit
OrderAnonymity on Market Liquidity. SIRCA Working Paper
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Thank you!