Measurement of Option Volatility Wrt Option Greek

8/7/2019 Measurement of Option Volatility Wrt Option Greek

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MeasurementofoptionvalueusingoptionGreeks

M.P.BIRLAINSTITUTEOFMANAGEMENT Page1

Measurement of Option VolatilityUsing Option Greeks

Submitted to

Bangalore University

In partial fulfillment ofthe requirements for the award

of the degree of

Masters of Business Administration

Under the guidance of

Prof. Praveen Bhagawan

Submitted By

Priyadarshini R

(Reg No. 06XQCM6063)

M.P. Birla Institute of ManagementAssociate Bharatiya Vidya Bhavan,

No 43, Race Course Road,Bangalore 560001


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DECLARATION

I hereby declare that this research project titled, Measurement of Option

Volatility Using Option Greeks is prepared under the guidance of Prof.

Praveen Bhagawan, Faculty, MPBIM, in partial fulfillment of Master of Business

Administration (MBA) program of Bangalore University at M. P. Birla Institute of

Management. This is my original work and has not been submitted for the award

of any other degree, diploma, fellowship or other similar title or prizes.

Place: Bangalore PRIYADARSHINI R.

Date: 06XQCM6063


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PRINCIPALS CERTIFICATE

This is to certify that the internship report titled, Measurement of Option

Volatility Using Option Greeks has been prepared by Ms. Priyadarshini R,

bearing registration number 06XQCM6063, under the guidance of Prof. Praveen

Bhagawan, M P Birla Institute of Management, Associate Bhartiya Vidya Bhavan,

Bangalore. This has not formed a basis for the award of any degree/diploma for

any other university.

Place: Bangalore Principal

Date: Dr. N.S.Mallavalli


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GUIDES CERTIFICATE

This is to certify that the internship Report entitled, Measurement of Option

Volatility Using Option Greeks done by Priyadarshini R, bearing Registration

No.06XQCM 6063 is a bonafide work done under my guidance in a partial

fulfillment of the requirement for the award of MBA degree by Bangalore

University. To the best of my knowledge this report has not formed the basis for

the award of any other degree.

Place: Bangalore Prof. Praveen Bhagawan

Date: (internal guide)


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ACKNOWLEDGEMENT

I am thankful to Dr.N.S.Malavalli, Principal, M.P.Birla institute of management,

Bangalore, who has given his valuable support during my project.

I am extremely thankful to Prof. Praveen Bhagwan, M.P.Birla institute of

Management, Bangalore, who has guided me to do this project by giving

valuable suggestions and advice.

Finally, I express my sincere gratitude to all my friends and well wishers who

helped me to do this project.

PRIYADARSHINI. R


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TABLE OF CONTENTS

CHAPTERS PARTICULARS PAGE

NUMBER

1 REAEARCH EXTRACT 1

2 INTRODUCTION 3

3 LITERATURE REVIEW 20

4 RESEARCH METHODOLOGY 28

5 SECTORAL ANALYSIS 31

6 DATA INTERPRETATION AND ANALYSIS 38

7 FINDINGS,CONCLUSION AND

SUGGESTIONS

64

BIBLIOGRAPHY

ANNEXURE


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LIST OF TABLES

TABLES PARTICULARS PAGENO

4.3 COMPANIES CONSIDERED UNDER BANKING INDUSTRY 30

4.3 COMPANIES CONSIDERED UNDER PHARMACEUTICALINDUSTRY

30

6.1 ANNUALISED VOLATILITY -BANKING INDUSTRY 39

6.2 ANNUALISED VOLATILITY-PHARMACEUTICAL INDUSTRY 39

6.3 ACTUAL AND THEORETICAL OPTION VALUES-BANKINGINDUSTRY

41

6.4 ACTUAL AND THEORETICAL OPTION VALUES-PHARMACEUTICAL INDUSTRY

42

THEORETICAL VALUES OF OPTION GREEKS

6.5 AXIS BANK 43

6.6 CENTRAL BANK 44

6.7 SYNDICATE BANK 45

6.8 FEDERAL BANK 46

6.9 YES BANK 48

6.10 DENA BANK 49

6.11 CANARA BANK 50


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6.12 CORPORATION BANK 51

6.13 UNION BANK 52

6.14 SUN PHARMACEUTICALS 54

6.15 DIVIS LABORATORIES 556.16 AUROBINDO PHARMACEUTICALS 56

6.17 BIOCON 57

6.18 RANBAXY 59

6.19 ORCHID CHEMICALS 60

6.20 STERLING BIOTECH 61

6.21 CIPLA LTD 62


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CHAPTER 1

RESEARCH EXTRACT


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1.1 RESEARCH EXTRACT

Volatility is the most important input in the pricing of an option. For a

sophisticated trader, option trading is volatility trading and the trader who can

forecast volatility the best is the most successful trader.

The objective of the study is to find the efficiency of the market participants in

forecasting the implied volatility using historical volatility. This is done by

considering 17 companies and their respective options from two different

industries i.e., banking and the pharmaceutical industries which are consistently

traded during the period of one month.

Using the different factors like strike price, share price, risk free rate of return and

theoretical volatility the values of option Greeks like delta, gamma, theta, vega

and rho for all seventeen stocks are calculated. The same is used to analyse the

different stocks. The theoretical volatilities calculated are compared with the

actual volatility. T-test is used for find out whether the difference between the

actual and the theoretical values are significant or not.

The findings of the study are the actual and theoretical values of options differ

significantly. The value of call option in case of any stock is completely influenced

by variations in option greeks i.e., Delta, Gamma, Theta, Gamma and Rho.


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CHAPTER 2INTRODUCTION


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2. DERIVATIVES

A derivative is a security or contract designed in such a way that its price is

derived from the price of an underlying asset. For instance, the price of a goldfutures contract for a certain maturity is derived from the price of gold. Changes

in the price of the underlying asset affect the price of the derivative security in a

predictable way.

2.1 DERIVATIVES MARKET

Derivative products initially emerged as hedging devices against fluctuations

in commodity prices, and commodity-linked derivatives remained the sole form of

such products for almost three hundred years. Financial derivatives came into

spotlight in the post-1970 period due to growing instability in the financial

markets. However, since their emergence, these products have become very

popular and by 1990s, they accounted for about two-thirds of total transactions in

derivative products.

In recent years, the market for financial derivatives has grown tremendously in

terms of variety of instruments available, their complexity and also turnover. In

the class of equity derivatives the world over, futures and options on stock

indices have gained more popularity than on individual stocks, especially among

institutional investors, who are major users of index-linked derivatives. Even

small investors find these useful due to high correlation of the popular indexes

with various portfolios and ease of use. The lower costs associated with index

derivatives visavis derivative products based on individual securities is anotherreason for their growing use.


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Derivative markets can broadly be classified as commodity derivative market and

financial derivatives markets. As the name suggest, commodity derivatives

markets trade contracts for which the underlying asset is a commodity. It can be

an agricultural commodity like wheat, soybeans, rapeseed, cotton, etc or

precious metals like gold, silver, etc. Financial derivatives markets trade

contracts that have a financial asset or variable as the underlying. The more

popular financial derivatives are those which have equity, interest rates and

exchange rates as the underlying. The most commonly used derivatives

contracts are forwards, futures and options which we shall discuss in detail later.

2.2 PARTICIPANTS IN THE DERIVATIVE MARKET

Participants who trade in the derivatives market can be classified under the

following three broad categories hedgers, speculators, and arbitragers.

HEDGERS: Hedgers face risk associated with the price of an asset. They use

the futures or options markets to reduce or eliminate this risk.

SPECULATORS: Speculators are participants who wish to bet on future

movements in the price of an asset. Futures and options contracts can give them

leverage; that is, by putting in small amounts of money upfront, they can take

large positions on the market. As a result of this leveraged speculative position,

they increase the potential for large gains as well as large losses.

ARBITRAGERS: Arbitragers work at making profits by taking advantage of

discrepancy between prices of the same product across different markets. If, for

example, they see the futures price of an asset getting out of line with the cash

price, they would take offsetting positions in the two markets to lock in the profit.


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2.3 KINDS OF FINANCIAL DERIVATIVES:

1) Forwards

2) Futures

3) Options

4) Swaps

5) Warrants

2.4 FORWARDS:

A forward contract refers to an agreement between two parties, to exchange an

agreed quantity of an asset for cash at a certain date in future at a predetermined

price specified in that agreement. The promised asset may be currency,

commodity, instrument etc.

In a forward contract, a user (holder) who promises to buy the specified asset at

an agreed price at a future date is said to be in the long position. on the other

hand one who promises to sell at an agreed price at a future date is said to be inshort position.

2.5 FUTURES:

A futures contract represents a contractual agreement to purchase or sell a

specified asset in the future for a specified price that is determined today. The

underlying asset could be foreign currency, a stock index, a treasury bill or any

commodity. The specified price is known as the future price. Each contract also

specifies the delivery month, which may be nearby or more deferred in time.


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The undertaker in a future market can have two positions in the contract: -

a) Long position is when the buyer of a futures contract agrees to purchase the

underlying asset.

b) Short position is when the seller agrees to sell the asset.

Futures contract represents an institutionalized, standardized form of forward

contracts. They are traded on an organized exchange, which is a physical place

of trading floor where listed contract are traded face to face.

A futures trade will result in a futures contract between 2 sides- someone going

long at a negotiated price and someone going short at that same price. Thus, if

there were no transaction costs, futures trading would represent a Zero sum

game what one side wins, which exactly match what the other side loses.

2.6 SWAPS:

Swaps are private agreements between two parties to exchange cash flows inthe future according to a prearranged formula. They can be regarded as

portfolios of forward contracts. The two commonly used swaps are:

INTEREST RATE SWAPS: These entail swapping only the interest

related cash flows between the parties in the same currency.

CURRENCY SWAPS: These entail swapping both principal and interest

between the parties, with the cash flows in one direction being in a

different currency than those in the opposite direction.


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2.7 SWAPTIONS:

Swaptions are options to buy or sell a swap that will become operative at the

expiry of the options. Thus a swaption is an option on a forward swap.

2.8 WARRANTS:

Options generally have lives of up to one year; the majority of options traded on

options exchanges having a maximum maturity of nine months. Longerdated

options are called warrants and are generally traded overthecounter.

2.9 INTODUCTION TO OPTIONS

An option contract is a contract where it confers the buyer, the right to either buy

or to sell an underlying asset (stock, bond, currency, and commodity) etc. at a

predetermined price, on or before a specified date in the future in return for the

guaranteeing the exercise of an option.

2.10 OPTION TRADING IN INDIAN MARKET:

Indian stock markets witnessed the introduction of derivative products like futures

and options during the years 2000 and 2001. Index futures were Introduced in

June 2000,followed by index options in June 2001. Stock options and futures

were introduced inJuly 2001 and November 2001, respectively.

Although derivative trading (including option trading) has been introduced both

on National Stock Exchange (NSE) and Bombay Stock Exchange (BSE), the

tradingvolumes are very low on BSE.


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There are two basic types of options that are traded in the market,

CALL OPTION: A call option gives the holder the right to buy the underlying

asset by a certain date for a certain price.

PUT OPTION: A put option gives the holder the right to sell the underlying asset

by a certain date for a certain price.

There is a further classification of options according to when they can be

exercised,

EUROPEAN OPTION: an option that can be exercised only on the expiration

date.

AMERICAN OPTION: a type of option that can be exercised on or before the

expiration date.

Apart from the above classifications, the options can also be classified intoexchange traded options and over the counter options.


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2.11 OPTIONS TERMINOLOGY

Option holder: the buyer of the option

Option writer: the seller of the option.

Option premium: option Premium is the price of an option. The premium is the

maximum loss that an option holder can incur. The option writer charges a

premium that reflects the calculation of the value of the underlying asset.

Exercise price or strike price: the fixed price at which the option holder can

buy and/or sell the underlying asset.

At the money: Options are said to be at the money when the exercise price of

the option equals the market price of the underlying asset.

In the money: a condition when,

Exercise price < market price for the call option

Exercise price > market price for the put option

Out of the money: a condition when,

Exercise price > market price for the call option

Exercise price < market price for the put option

Option premium = intrinsic value + time value


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2.12 OPTION GREEKS

The Greeks are a collection of statistical values (expressed as percentages) that

give the investor a better overall view of how a stock has been performing. These

statistical values can be helpful in deciding what options strategies are best to

use.

DELTA:

The Delta is a measure of the relationship between an option price and the

underlying stock price. Whenever one long a call option, delta will always be a

positive number between 0 and 1. When the underlying stock or futures contract

increases in price, the value of your call option will also increase by the call

options delta value. Conversely, when the underlying market price decreases the

value of your call option will also decrease by the amount of the delta.

NOTE: Long and short: Long refers to a position as the option holder. Shortrefers to a position as the option writer


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GAMMA:

Gamma, also known as the 'first derivative of delta', measures the rate of change

of delta.The gamma of a portfolio of options on an underlying asset may be

defined as the rate of change of the portfolios delta with respect to the price of

the underlying instrument. In other words, it is change in delta per unit change in

the price of the asset.

If the gamma is small and not significant it means that the delta changes only

very slowly then adjustments for keeping delta neutral need relatively

infrequently. On the other hand, if the gamma is very high which means that delta

is highly sensitive to stock price then in that case the adjustment to make delta

neutral is immediate needed.

The gamma value is always positive and varies with stock prices. At the money

option, gamma increases as the time to maturity decreases. It is further noticed

that the short life at-the-money options have very high gamma which shows thatthe value of the option holders position is highly sensitive to jumps in the stock

price.The gamma of an option indicates how the delta of an option will change

relative to a 1 point move in the underlying asset. In other words, the Gamma

shows the option delta's sensitivity to market price changes


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The above graph shows Gamma vs. Underlying price for 3 different strike prices.

It can be seen that the Gamma increases as the option moves from being in-the-

money reaching its peak when the option is at-the-money. Then as the option

moves out-of-the-money the Gamma then decreases.

THETA:

Theta refers to the rate of time decay for an option. It is the first differential of the

option value with respect to time. Holding all other things constant, an option

loses value as it approaching to the expiration day.

Option values increase with the length of time to maturity. The expected change

in the option premium from a small change in the time to expiration is termed as

theta. In other words, it is a rate of change in the option portfolio value as time

passes. It is also called time delay of the portfolio.

The option premium deteriorates at an increasing rate as they approach

expiration. It is also observed that most of the option premiums, depending on

the individual option premium, depending on the individual option, is lost in the

final 30 days prior to expiration. That is why; theta is based not on al linear

relationship with time, but rather on the square root of time. This exponential


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relationship between option premium and time is seen in the ratio of option value

between the four-month and the one-month at-the-money maturities. It will be:

= (Premium of four months/Premium of one month)

= (SQRT OF 4/SQRT OF 1)

= (2/1)

= 2

Theta shows how much value the option price will lose for every day that passes

.

Vega:

Vega may be defined as the rate of change of the value of the portfolio of optionswith respect to change in volatility of the underlying asset. It is the first

differential of the option price with respect to the volatility (standard deviation).

The more volatility the underlying asset is, the more valuable the option becomes

since the chance for the option to be deep-in-the-money is greater.


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Vega is also referred as lambda, kappa, or sigma. Volatility is stated in

percentage per annum. Volatility is defined as the standard deviation of daily

percentage change in the underlying stock price.

In practice, volatility changes over time. This means that the value of an option is

liable to change because of movements in stock prices over the passage of time.

If Vega is high in absolute terms, the portfolio value is very sensitive to change

in volatility. The sensitivity of the option premium to a unit change in volatility is

termed as lambda or vega.

The Vega of an option indicates how much, theoretically at least, the price of the

option will change as the volatility of the underlying asset changes.


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2.13 MATHEMATICAL REPRESENTATION OF OPTION GREEKS

Where,C = value of the call option

St = current value of the underlying asset

X = exercise price or strike price

Rf = risk free return

T = option life as percentage of year

= standard deviation of the growth rate on the underlying asset

= pie value

N(d1) = the rate of change of option price with respect to the price of the

underlying asset.

N(d2) = probability of the option being in the money.

The above formulae holds good for put options also.


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2.14 BLACK SCHOLES FORMULA:

C=S[N(d1)] Ke-rt [N(d

2)]

Where,

C= call premium

S=current stock price

t=time until option expiration

K=option striking price

r=risk free interest returnN=cumulative standard normal distribution


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The call option price is calculated using Black Scholes equation and the option

Greeks values are estimated .The difference between the theoretical option value

and the actual option value signifies volatility arising due to various factors. The

same is measured effectively using the option Greeks.

2.15 CALCULATION OF THEORETICAL VOLATILITY

The annualized volatility is the standard deviation of the instrument'slogarithmic returns in a year.

It can be represented as follows,

where the preceding superscript t1 indicates that the standard deviation is

conditional on information available at time t1

Historical volatilities are usually calculated from daily and monthly data. Because

volatilities are usually quoted on an annual basis (especially for option pricing)

such daily historical volatilities are routinely converted to an annual basis by

applying the square root of time rule. This is done even if conditions for

applying that rule are not satisfied. The resulting volatilities are referred to as

annualized volatilitiesas opposed to annual volatilitiesto alert people to the

fact that this is just a quoting convention.


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2.16 STATEMENT OF THE PROBLEM:

Options value or option premium changes with movements in the underlying

stock price, risk free rate, exercise price, time to maturity, variance of the returns

etc which affects the market participants like general investors and retail traders

profit. Volatility is one of the most important inputs in the pricing of an option.

Measuring the volatility using the option Greeks is the consideration of the study.

2.17 OBJECTIVES OF THE STUDY

To measure the option volatility using option Greeks.

To find out the impact of fluctuations of stock price, exercise price, time to

maturity, risk free rate, variance of the returns etc on the option premium.

To compare the theoretical option values with the actual option values in

order to find out the deviations caused due to volatility.

2.18 LIMITATIONS OF THE STUDY

The study is limited to 17 companies options only.

The study is limited to a period of one month only.


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CHAPTER 3

LITERATURE REVIEW


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3.1 LITERATURE REVIEW:

The purpose if literature review is to find out the various studies that have been

done in the relative fields of the present study and also to understand the various

methodologies followed by the authors to arrive at the conclusions.

The following are some of the related studies:

According to Nagaraj KS and Kotha Kiran Kumar (1) it is understood that studies

on the impact of the introduction of futures on the volatility of the underlying index

report no increase in the spot volatility after the introduction of futures. However,

prior studies do not comment on how exactly the information transmits from the

futures market to the spot market.

The paper focuses on investigating whether the change in the structure of spot

volatility evolution process is due to the futures trading activity. The relation

between the Futures Trading Activity (measured through trading volume andopen interest) and spot index volatility is documented, following Bessembinder

and Seguin (1992), by partitioning trading activity into expected and shock

components by an appropriate ARMA model

.

The series are then appended in the variance equation through an appropriate

ARMAGARCH model, following Gulen and Mayhew (2000). Further, the study

examines the effect of the September 11 terrorist attack on the Nifty spot-futures

relation.that post the September 11 attack, the relation between Futures Trading

Activity and Spot volatility has strengthened, implying that the market has

become more efficient in assimilating the information into its prices monthly and

daily volatility proxies. These studies support the Non-Destabilization hypothesis

i.e., there is no increase in the spot volatility after the futures introduction.


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However, these studies, except Premalatha (2003), do not comment on how

exactly the information transmits from the futures market to the spot market.

Premalatha (2003) touches upon this issue but does not provide conclusive

evidence on significance of futures trading activity on spot index volatility. This

paper investigates whether the changes in the structure of spot volatility evolution

process are due to futures trading activity. Futures trading activity is measured

through trading volume (total number of contracts traded) and open interest (total

number of outstanding long/short contracts). Unlike in the spot market, where the

number of shares in existence on a day is given, in futures market the number of

contracts in existence i.e. opens interest, changes on a continuous basis. Hence,

open interest is taken along with trading volume as a trading activity variable.

The relation between Futures Trading Activity and Spot Index volatility is

documented following Bessembinder and Seguin (1992) by decomposing

Trading Volume and Open Interest into expected (predictable) and unexpected

(shock) series using an appropriate ARMA model. These are then appended in

the variance (volatility) equation of NSE Nifty spot index volatility through anappropriate ARMA-GARCH model.

The study also focuses on the effect the September 11th terrorist attack has had

on the Nifty spot-futures relation by incorporating a dummy variable in the

GARCH equation.

The 9/11 event has increased the trading in the futures market drastically.

Changes in futures are expected to affect the spot market due to the close

linkages between these two markets. It is found that both volume and open

interest (expected and activity shock) are significant post September 11 while not

being significant pre September 11, implying that the market has become more

efficient in absorbing the information.


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According to Manisha Joshi and Chiranjit Mukhopadhyay* (2)In there paper an

attempt has been made to assess the impact of recently introduced .options. on

the underlying stock of a company in the Indian equity markets. The effect of

option introduction on the simple and continuously compounded return volatility,

measured by the stock return variance, is examined for the initial 29 stocks on

which options were first introduced on July 2, 2001 on the National Stock

Exchange (NSE).

Numerous studies performed in the developed markets for the same problem

have presented contradictory results. The derivatives market is still nascent in

India, and so far, to the authors. Knowledge, no study has looked into this issue

at the individual security level. In this paper, both conditional and marginal return

volatilities before and after option introduction are first extracted by fitting

appropriate ARMA models for the two periods.

Then these models are utilized to investigate any change in marginal volatility

using standard large sample tests, such as Walds test, Likelihood Ratio Test and

Lagrange Multiplier Test apart from the usual F-test, which is usually erroneouslyused, for checking the equality of variances in such situations. However, the

change in conditional volatilities is checked using an F-test for comparing two

innovation variances. The initial findings suggest that there is no significant

change in the mean returns. The volatility exhibits a change but the results are

not significant, suggesting that option introduction has had no effect on the

volatility of the underlying stock.

In the Indian context, three studies have been conducted so far to study the

effect of introduction of derivatives on the underlying spot market.

Shenbagaraman (2003) looked at the S&P CNX Nifty index futures and index

options contracts that are traded on the National Stock Exchange (NSE), India.

She used a univariate GARCH model to estimate the volatility and found that


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futures and options trading has not led to a change in the Volatility of the

underlying stock index, but detected a change in the nature of the volatility.

Gupta and Kumar (2002) also looked at the effect of introduction of index futures

on the underlying S&P CNX Nifty. They constructed three different measures of

volatility and used the F-test to check for differences between the before and

after estimates of the volatility.

Thenmozhi (2002) also looked at the effect of introduction of index futures on the

volatility of the underlying stock index and used a GARCH model for the same.

Thus we find a lot of contradictory findings in the literature in relation to the effect

of option introduction on the underlying stock. Given the ambiguity in the findings

of the previous studies, this paper aims to examine the impact of introducing

options in the Indian context. It tries to discover how the volatility of returns of

underlying stocks is getting affected due to the introduction of options that are

traded on the National Stock Exchange. The paper attempts to model the extent

to which the mean and marginal and conditional volatility of underlying stock

returns have changed since the introduction of options. The study finds that there

is no significant change in any of these characteristics, if one applies anappropriate methodology, as developed in this article. However, the erroneous F-

test would have led one to believe otherwise.

According to James B. WIGGINS (3) he numerically solves the call option

valuation problem given a fairly general continuous stochastic process for return

volatility. Statistical estimators for volatility process parameters are derived, and

parameter estimates are calculated for several individual stocks and indices. The

resulting estimated option values do not differ dramatically from Black-Scholes

values in most cases, although there is some evidence that for longer-maturity

index options, Black-Scholes overvalues out-of-the-money calls in relation to in-

the-money calls.


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Several authors have developed option-pricing formulas under alternate

assumptions about the underlying assets return distribution. The models of

Merton (1976). Cox and Ross (1976) and Jones (1983) allow for a Poisson

process in security returns. Cox (1975) Geske (1979), and Rubinstein (1983)

derive formulas in which return variance can be a function of the stock price. On

the empirical front, Mandelbrot (1963), Fama (1965), and Blattberg and Gonedes

(1974) found the stationary (1og)normal distribution to be an inadequate

descriptor of stock returns, and have fitted various alternate stationary

distributions to the data. More recently, Hsu, Miller and Wichem (1974)

Westerfield (1977) and Kon (1984) have found that a mixture of normals does a

better job of describing leptokurtic empirical distributions than do a number of

stationary alternatives. Others, including Oldfield, Rogalski and Jarrow (1977),

Rosenfeld (1980) and Ball and Torous (1985) have empirically estimated models

of returns as mixtures of continuous and jump processes.

Several authors have investigated the time-series properties of (estimated)stock-return volatilities. Black (1976), Schmalensee and Trippi (1978), Beckers

(1980), and Christie (1982) have uncovered a pervasive imperfect inverse

correlation between stock returns and changes in volatility, at least partly

attributable to real and financial leverage effects. Black (1976), Poterba and

Summers (1984), and Beckers (1983) provide evidence that shocks to volatility

persist but tend to decay over time. Existing option-valuation models cannot fully

incorporate the above empirical regularities of volatility behavior.


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The option-valuation model presented in this paper assumes return volatility

follows a fairly general continuous process, allowing for an imperfect

return/volatility correlation and mean reversion in volatility. It can thus help

determine the robustness of existing formulas to alternate underlying return

processes. But given the elegance and tractability of the Black-Scholes formula,

profitable application of alternate models requires that economically significant

valuation improvements can be obtained empirically.

In other words, the empirical variance of the variance, and its correlation with

returns, must be large enough to produce major deviations from log normality

and thus (perhaps) major option valuation discrepancies before more

complicated models are justified. To see whether the stochastic volatility model

may have some practical applicability, I empirically estimate a model of the

volatility process for a number of individual equities and stock indices, and

calculate option values based on the parameter estimates.

BlackScholes model (4) Robert C. Merton was the first to publish a paper

expanding our mathematical understanding of the options pricing model andcoined the term "Black-Scholes" options pricing model, by enhancing work that

was published by Fischer Black and Myron Scholes. It is somewhat unfair to

Merton that the resulting formula has ever since been known as Black-Scholes,

but with another hyphen the label would be unwieldy. The paper was first

published in 1973. The foundation for their research relied on work developed by

scholars such as Louis Bachelier, A. James Boness, Edward O. Thorp, and Paul

Samuelson. The fundamental insight of Black-Scholes is that the option is

implicitly priced if the stock is traded Merton and Scholes received the 1997

Nobel Prize in Economics for this and related work; Black was ineligible, having

passed away in 1995.


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In this paper, both conditional and marginal return volatilities before and after

option introduction are first extracted by fitting appropriate ARMA models for the

two periods. Then these models are utilized to investigate any change in

marginal volatility using standard large sample tests, such as Walds test,

Likelihood Ratio Test and Lagrange Multiplier Test apart from the usual F-test,

which is usually erroneously used, for checking the equality of variances in such

situations. However, the change in conditional.

Volatilities is checked using an F-test for comparing two innovation variances.

The initial findings suggest that there is no significant change in the mean

returns. The volatility exhibits a change but the results are not significant,

suggesting that option introduction has had no effect on the volatility of the

underlying stock.


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CHAPTER 4

RESEARCH METHODOLOGY


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4.1 STUDY DESIGN

STUDY TYPE: The study type is analytical, quantitative and historical. Analytical

because facts and existing information is used for the analysis, Quantitative as

relationship is examined by expressing variables in measurable terms and also

Historical as the historical information is used for analysis and interpretation.

SAMPLING TECHNIQUE: Deliberate sampling is used because only particular

units are selected from the sampling frame. Such a selection is undertaken as

these units represent the population in a better way and reflect better relationship

with the other variable.

SAMPLE SIZE: Sample chosen is options of 17 companies from two different

industries from Nifty 50 for the period started from 14-2-2008 to 14-3-2008.

STUDY POPULATION: population is the entire Options market.

SAMPLING FRAME: Sampling Frame would be Indian stock Options market.

4.2 DATA GATHERING PROCEDURES AND INSTRUMENTS:

DATA AND DATA SOURCE: Historical options prices and Historical daily prices

of underlying stock, MIBOR risk free rate of return, actual option values have

been taken from NSE website (www.nseindia.com) and capitaline database.

Data collected was of 17 stocks from 2 different industries i.e., banking and the

pharmaceutical industries and their respective options for the period of one

month.


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4.3 SCOPE OF THE STUDY

The scope of the study extends till the preview of 17 stocks from two different

industries and their respective options traded consistently during the period of

one month (feb 14th to mar 14th) in National Stock Exchange of India.

Banking industry

1. Axis bank

2. Canara bank

3. Central bank

4. Corporation bank

5. Dena bank

6. Federal bank

7. Syndicate bank

8. Union bank

9. Yes bank

Table 4.1

Pharmaceutical industry

1. Sun pharmaceuticals ltd

2. Ranbaxy laboratories

3. Cipla laboratories ltd

4. Biocon ltd

5. Aurobindo pharmaceuticals ltd

6. Divis laboratories

7. Sterling biotech

8. Orchid chemicals

Table 4.2


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.

CHAPTER 5

SECTORAL ANALYSIS


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5.1SECTORAL ANALYSIS

BANKING SECTOR

The Indian Banking industry, which is governed by the Banking Regulation Act of

India, 1949 can be broadly classified into two major categories, non-scheduled

banks and scheduled banks. Scheduled banks comprise commercial banks and

the co-operative banks. In terms of ownership, commercial banks can be further

grouped into nationalized banks, the State Bank of India and its group banks,

regional rural banks and private sector banks (the old/ new domestic and

foreign). These banks have over 67,000 branches spread across the country.

The first phase of financial reforms resulted in the nationalization of 14 major

banks in 1969 and resulted in a shift from Class banking to Mass banking. This in

turn resulted in a significant growth in the geographical coverage of banks. Every

bank had to earmark a minimum percentage of their loan portfolio to sectorsidentified as priority sectors. The manufacturing sector also grew during the

1970s in protected environs and the banking sector was a critical source. The

next wave of reforms saw the nationalization of 6 more commercial banks in

1980. Since then the number of scheduled commercial banks increased four-

foldand the number of bank branches increased eight-fold.

After the second phase of financial sector reforms and liberalization of the sector

in the early nineties, the Public Sector Banks (PSB) s found it extremely difficult

to compete with the new private sector banks and the foreign banks. The new

private sector banks first made their appearance after the guidelines permitting

them were issued in January 1993. Eight new private sector banks are presently

in operation. These banks due to their late start have access to state-of-the-art


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technology, which in turn helps them to save on manpower costs and provide

better services

Ever since Indian economy opened its doors to MNCs, the Indian banking sector

has been witnessing bizarre changes in terms of new products and services and

stiff competition as well. The sort of IPOs that have been taking place in banking

sector are amazing.

An analysis of Indian Banking sector :

The Reserve Bank of India (RBI), as the central bank of the country,

closely monitors developments in the whole financial sector.

The banking sector is dominated by Scheduled Commercial Banks (SCBs).

As at end-March 2002, there were 296 Commercial banks operating in India.

This included 27 Public Sector Banks (PSBs), 31 Private, 42 Foreign and 196

Regional Rural Banks. Also, there were 67 scheduled co-operative banks

consisting of 51 scheduled urban co-operative banks and 16 scheduled state

co-operative banks.

Scheduled commercial banks touched, on the deposit front, a growth of 14%

as against 18% registered in the previous year. And on advances, the growth

was 14.5%against 17.3 % of the earlier year.

State Bank of India is still the largest bank in India with the market share of

20%. ICICI and its two subsidiaries merged with ICICI Bank, leading creating

the second largest bank in India with a balance sheet size of Rs1040bn.

Higher provisioning norms, tighter asset classification norms, dispensing with

the concept of past due for recognition of NPAs, lowering of ceiling on

exposure to a single borrower and group exposure etc., are among the

important measures in order to improve the banking Sector.


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A minimum stipulated Capital Adequacy Ratio (CAR) was introduced to

strengthen the ability of banks to absorb losses and the ratio has

subsequently been raised from 8% to 9%. It is proposed to hike the CAR to

12% by 2004 based on the Basle Committee recommendations.

Retail Banking is the new mantra in the banking sector. The home loans

alone account for nearly two-third of the total retail portfolio of the bank.

According to one estimate, the retail segment is expected to grow at 30-40%

in the coming years.

Net banking, phone banking, mobile banking, ATMs and bill payments are the

new buzz words that banks are using to lure customers.

With a view to provide an institutional mechanism for sharing of information

on borrowers/ potential borrowers by banks and Financial Institutions, the

Credit Information Bureau (India) Ltd. (Cibil) was set up in August 2000.

The RBI is now planning to transfer of its stakes in the SBI, NHB and NationalBank for Agricultural and Rural Development to the private players. Also, the

Government has sought to lower its holding in PSBs to a minimum of 33 per

cent of total capital by allowing them to raise capital from the market.

Banks are free to acquire shares, convertible debentures of corporates and

units of equity-oriented mutual funds, subject to a ceiling of 5% of the total

outstanding advances (including Commercial Paper) as on March 31 of the

previous year.


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The finance ministry spelt out structure of the government-sponsored ARC

called the Asset Reconstruction Company (India) Limited (Arcil), this pilot

project of the ministry would pave way for smoother functioning of the credit

market in the country. The Government will hold 49% stake and private

players will hold the rest 51% - the majority being held by ICICI Bank (24.5%).

PHARMACEUTICAL SECTOR

The Indian pharmaceutical industry currently tops the chart amongst India'sscience-based industries with wide ranging capabilities in the complex field of

drug manufacture and technology. A highly organized sector, the Indian

pharmaceutical industry is estimated to be worth $ 4.5 billion, growing at about 8

to 9 percent annually. It ranks very high amongst all the third world countries, in

terms of technology, quality and the vast range of medicines that are

manufactured. It ranges from simple headache pills to sophisticated antibiotics

and complex cardiac compounds; almost every type of medicine is now made in

the Indian pharmaceutical industry.

The Indian pharmaceutical sector is highly fragmented with more than 20,000

registered units. It has expanded drastically in the last two decades. The

Pharmaceutical and Chemical industry in India is an extremely fragmented

market with severe price competition and government price control. The

Pharmaceutical industry in India meets around 70% of the country's demand for

bulk drugs, drug intermediates, pharmaceutical formulations, chemicals, tablets,capsules, orals and injectibles. There are approximately 250 large units and

about 8000 Small Scale Units, which form the core of the pharmaceutical

industry in India (including 5 Central Public Sector Units).


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Playing a key role in promoting and sustaining development in the vital field of

medicines, Indian Pharma Industry boasts of quality producers and many units

approved by regulatory authorities in USA and UK. International companies

associated with this sector have stimulated, assisted and spearheaded this

dynamic development in the past 53 years and helped to put India on the

pharmaceutical map of the world

The Indian Pharmaceutical sector is highly fragmented with more than 20,000

registered units. It has expanded drastically in the last two decades. The leading

250 pharmaceutical companies control 70% of the market with market leader

holding nearly 7% of the market share. It is an extremely fragmented market with

severe price competition.

The pharmaceutical industry in India meets around 70% of the country's demand

for bulk drugs, drug intermediates, pharmaceutical formulations, chemicals,

tablets, capsules, orals and injectibles. There are about 250 large units and

about 8000 Small Scale Units, which form the core of the pharmaceutical

industry in India (including 5 Central Public Sector Units). These units produce

the complete range of pharmaceutical formulations, i.e., medicines ready for

consumption by patients and about 350 bulk drugs, i.e., chemicals having

therapeutic value and used for production of pharmaceutical formulations.

Following the de-licensing of the pharmaceutical industry, industrial licensing for

most of the drugs and pharmaceutical products has been done away with.

Manufacturers are free to produce any drug duly approved by the Drug Control

Authority. Technologically strong and totally self-reliant, the pharmaceutical

industry in India has low costs of production, low R&D costs, innovative scientificmanpower, strength of national laboratories and an increasing balance of trade.

The Pharmaceutical Industry, with its rich scientific talents and research

capabilities, supported by Intellectual Property Protection regime is well set to

take on the international market


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The Indian pharmaceutical industry currently tops the chart amongst India's

science-based industries with wide ranging capabilities in the complex field of

drug manufacture and technology. A highly organized sector, the Indian

pharmaceutical industry is estimated to be worth $ 4.5 billion, growing at about 8

to 9 percent annually. It ranks very high amongst all the third world countries, in

terms of technology, quality and the vast range of medicines that are

manufactured. It ranges from simple headache pills to sophisticated antibiotics

and complex cardiac compounds; almost every type of medicine is now made in

the Indian pharmaceutical industry.

The Indian pharmaceutical sector is highly fragmented with more than 20,000

registered units. It has expanded drastically in the last two decades. The

Pharmaceutical and Chemical industry in India is an extremely fragmented

market with severe price competition and government price control. The

Pharmaceutical industry in India meets around 70% of the country's demand for

bulk drugs, drug intermediates, pharmaceutical formulations, chemicals, tablets,

capsules, orals and injectibles.


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CHAPTER 6

PRESENTATION

AND

ANALYSIS OF DATA AND

INTERPRETATION


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6.1 THE ANNUALISED VOLATILITY CALCULATED FOR DIFFERENT

COMPANIES ARE TABULATED BELOW:

BANKING INDUSTRY ANNUALISED VOLATILITY

AXIS BANK 0.630517844

FEDERAL BANK 0.326251461

CENTRAL BANK 0.541048328

DENA BANK 0.480896226

SYNDICATE BANK 0.478573746

UNION BANK 0.68070983

YES BANK 0.704445838

CANARA BANK 0.547133375

CORPORATION BANK 0.553831789

Table 6.1

PHARMACEUTICAL INDUSTRY ANNUALISED VOLATILTY

SUN PHARMA 0.530041499

RANBAXY 0.351471519

CIPLA 0.40767836

BIOCON 0.382300502

AUROBINDO 0.424693418DIVIS LABORATORIES 0.452418014

STERLING BIOTECH 0.29456265

ORCHID CHEMICALS 0.393342238


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Table 6.2

In the case of options most of the trading takes place in the near-month options

i.e., those options which are maturing within one month. Therefore, only those

call options, which have term to maturity as one month, are considered. Similarly,

the trading data is available for call options with different strike prices. The strike

price for which volume of trading is highest as on march 14th is considered for the

study. MIBOR risk free interest rate as on 14 th march is used.

Using this data on strike price, stock price, term to maturity and risk-free interest

rate and closing prices of call options, theoretical option value is calculated using

Black Scholes formula.


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6.2 T-TEST:

This test is conducted to find the relationship between actual and the theoretical

option values.

Hypothesis:

H0 =actual and theoretical volatilities does not differ significantly.

H1 = actual and theoretical volatilities differ significantly.

BANKING INDUSTRY ACTUAL

OPTION VALUE

THEORETICAL

OPTION VALUE

AXIS BANK 95.25 65.698

CANARA BANK 27.50 39.699

CENTRAL BANK 0.40 0.145

CORP BANK 22.40 16.888

DENA BANK 1.95 1.264

FEDERAL BANK 44.85 6.985

SYNDICATE BANK 2.30 2.798

UNION BANK 17.40 12.238

YES BANK 3.65 11.922

Table 6.3

INTERPRETATION

T tabulated value for 16 degrees of freedom is 0.744906. The corresponding P

value obtained is 0.46713. Therefore, Null Hypothesis is accepted which infers

that the actual and the theoretical option values do not differ significantly.


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PHARMACEUTICAL

INDUSTRY

ACTUAL OPTION

VALUE

THEORETICAL

OPTION VALUE

SUN PHARMA 87.00 84.92RANBAXY 23.40 13.653

CIPLA 4.65 8.388

BIOCON 71.80 20.068

AUROBINDO 72.35 14.619

DIVIS LAB 186.45 70.575

STERLING BIOTECH 24.35 5.503

ORCHID CHEMICALS 38.60 11.340

Table 6.4

INTERPRETATION:

T tabulated value for 14 degrees of freedom is 1.517119. The corresponding P

value obtained is 0.15149. Therefore, Null Hypothesis is accepted which infers

that the actual and the theoretical option values do not differ significantly.


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6.3 The theoretical values of option Greeks and its interpretations

BANKING SECTOR

1. AXIS BANK

Option Value 65.698 Delta: 0.554 Theta: -409.70 Rho1 34.249

% of share: 7.6 Gamma: 0.0025 Vega: 98.171 Rho2 -39.72

Table 6.5

Option Value = 65.698

This is the theoretical (or fair) value of the option, and should be compared

with the actual trading price of the option in the market.

% of share = 7.6

This is simply the option value 65.698 expressed as a percentage of the

share price 860.350

Delta = 0.554

If the share price changes by a small amount, then the option price should

change by 55.41 % of that amount.

Gamma = 0.002524

If the share price changes by a small amount, then the delta should

change by 0.002524 times that amount. If the share price increased by 1,

then the delta should change by 0.002524.

Theta = -409.702

If the time to maturity changes by a small amount, then the option valueshould change by -409.70 times that amount.


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Vega = 98.171

If the volatility changes by a small amount, then the option value should

change by 98.17 times that amount. For example, if the volatility increased

by 0.01 (from 20-21%), then the option value should change by 0.982.

Rho1 = 34.249

If the risk-free interest rate changes by a small amount, then the option

value should change by 34.25 times that amount. For example, if the risk-

free interest rate increased by 0.01 (from 6-7%), the option value would

change by 0.342.

2. CENTRAL BANK

Option Value 0.145 Delta: 0.031 Theta: -5.532 Rho1: 0.198

% of share: 0.2 Gamma 0.00558 Vega: 1.636 Rho2: -0.210

Table 6.6




% of share = 0.2


share price 80.600

Delta = 0.031


change by 3.12 % of that amount. For example, if a european call option

on 100,000 shares is sold, then 3121 shares must be bought to hedge the

position.


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Gamma = 0.005585


change by 0.005585 times that amount. For example, if the share price

increased by 1, then the delta should change by 0.005585.

Theta = -5.532

If the time to maturity changes by a small amount, then the option value

should change by -5.53 times that amount.

Vega = 1.636




Rho1 = 0.198




change by 0.002

3. SYNDICATE BANK


% of share: 3.7 Gamma: 0.03686 Vega: 8.492 Rho2: -2.551

Table 6.7




% of share = 3.7


share price 76.000


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Delta = 0.403


change by 40.29 % of that amount. For example, if a European call option

on 100,000 shares is sold, then 40285 shares must be bought to hedge

the position.

Gamma = 0.036864




Theta = -26.977



Vega = 8.492




Rho1 = 2.318If the risk-free interest rate changes by a small amount, then the option



change by 0.023

4. FEDERAL BANK



Table 6.8


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% of share = 2.9


share price 242.150

Delta = 0.434




the position.

Gamma = 0.017252




Theta = -62.983If the time to maturity changes by a small amount, then the option value


Vega = 27.503




Rho1 = 8.177




change by 0.082.


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5. YES BANK

Option Value 11.922 Delta: 0.485 Theta: -91.215 Rho1: 6.030% of share: 6.9 Gamma 0.0112 Vega: 19.985 Rho2: -7.023

Table 6.9




% of share = 6.9


share price 173.650

Delta = 0.485




the position.

Gamma = 0.011290




Theta = -91.215



Vega = 19.985





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Rho1 = 6.030




change by 0.060.

6. DENA BANK



Table 6.10




% of share = 2.2


share price 58.700

Delta = 0.271




the position.

Gamma = 0.040670





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Theta = -17.571



Vega = 5.616




Rho1 = 1.222




change by 0.012.

7. CANARA BANK



Table 6.11




% of share = 17.9


share price 222.350

Delta = 0.634


change by 63.36 % of that amount.


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Gamma = 0.004375




Theta = -41.807



Vega = 59.173



by 0.01 (from 20-21%), then the option value should change by 0.592 .

Rho1 = 50.590




change by 0.506.

8. CORPORATION BANK

Option Value 16.888 Delta: 0.546 Theta -108.105 Rho1: 10.166


Table 6.12




% of share = 6.6


share price 254.450


60/81



Delta = 0.546




the position.

Gamma = 0.009742



increased by 1, then the delta should change by 0.009742 .

Theta = -108.105



Vega = 29.110




Rho1 = 10.166

If the risk-free interest rate changes by a small amount, then the optionvalue should change by 10.17 times that amount. For example, if the risk-


change by 0.102.

9. UNION BANK


% of share: 8.4 Gamma: 0.013760 Vega: 16.559 (Rho2): -6.843

Table 6.13


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% of share = 8.4


share price 145.650

Delta = 0.564




the position.

Gamma = 0.013760



increased by 1, then the delta should change by 0.013760 .

Theta = -74.145


should change by -74.14 times that amount.Vega = 16.559




Rho1 = 5.823




change by 0.058.


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PHARMACEUTICAL SECTOR

1. SUN PHARMACEUTICALS

Option Value 84.92 Delta 0.556 Theta: -527.847 Rho1: 52.810


Table 6.14




% of share = 6.6


share price 1292.650

Delta = 0.556




the position.

Gamma = 0.001997




Theta = -527.847




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Vega = 147.402


change by 147.40 times that amount. For example, if the volatility

increased by 0.01 (from 20-21%), then the option value should change by

1.474.

Rho1 = 52.810


value should change by 52.81 times that amount. If the risk-free interest

rate increased by 0.01 (from 6-7%), the option value would change by

0.528.

2. DIVIS LABORATORIES



Table 6.15




% of share = 5.7


share price 1233.450

Delta = 0.558




the position.


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Gamma = 0.002450




Theta = -439.089



Vega = 140.539


change by 140.54 times that amount. For example, if the volatility

increased by 0.01 (from 20-21%), then the option value should change by

1.405.

Rho1 = 51.487




change by 0.515

3. AUROBINDO PHARMACEUTICALS



Table 6.16




% of share = 5.1


65/81




share price 288.800

Delta = 0.536




the position.

Gamma = 0.011221




Theta = -97.474



Vega = 33.123


change by 33.12 times that amount. For example, if the volatility increasedby 0.01 (from 20-21%), then the option value should change by 0.331.

Rho1 = 11.686


value should change by 11.69 times that amount.

4. BIOCON

Option Value 20.06 Delta 0.542 Theta: -132.53 Rho1: 17.724


Table 6.17


66/81






% of share = 4.7


share price 429.100

Delta = 0.542




the position.

Gamma = 0.008377




Theta = -132.538


should change by -132.54 times that amount.Vega = 49.137




Rho1 = 17.724




change by 0.177


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5. RANBAXY

Option Value 13.65 Delta: 0.421 Theta: -127.50 Rho1: 15.152% of share: 2.9 Gamma 0.0083 Vega: 52.424 Rho2: -16.29

Table 6.18




% of share = 2.9


share price 464.350

Delta = 0.421




the position.

Gamma = 0.008301




Theta = -127.503



Vega = 52.424





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Rho1 = 15.152




change by 0.152

6. ORCHID CHEMICALS



Table 6.19




% of share = 5.5


share price 207.250

Delta = 0.588




the position.

Gamma = 0.016542




Theta = -65.261




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Vega = 23.290




Rho1 = 9.203




change by 0.092.

7. STERLING BIOTECH



Table 6.20




% of share = 3.5


share price 159.000

Delta = 0.524




the position.


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Gamma = 0.029454


change by 0.029454

Measurement of Option Volatility Wrt Option Greek

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