For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425

8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425

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FORECASTING VOLATILITY IN OPTION TRADING

M. P BIRLA INSTITUTE OF MANAGEMENT 1


A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF

MBA DEGREE OF BANGALORE UNIVERSITY

SUBMITTED BY

MADHURI ANUMALASETTY Reg. No 04XQCM6047

UNDER THE GUIDANCE OF Dr.NAGESH MALAVALLI

MPBIM (INTERNAL GUIDE)

M. P. BIRLA INSTITUTE OF MANAGEMENT(ASSOCIATE BHARATIYA VIDYA BHAVAN)# 43, Race Course Road, BANGALORE 560001

Tel: 080-22382798, 080-22389635(2004-2006 Batch)


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DECLARATION

I hereby declare that the research work embodied in this dissertation titled FORECASTING VOLATILITY IN OPTION TRADING has been carried out by

me under the guidance and supervision of Dr.NAGESH MALAVALLI (Internal Guide),

M.P.Birla Institute of Management, Bangalore. I also declare that this dissertation has not

been submitted to any other university/ Institution for the award of any other

Degree/Diploma.

Place: Bangalore (MADHURI ANUMALASETTY)

Date: Reg No: 04XQCM6047


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GUIDE S CERTIFICATE

This is to certify that this report titled FORECASTING VOLATILITY IN OPTION

TRADING has been prepared by Ms. MADHURI ANUMALASETTY of M. P. Birla

Institute of Management, Bangalore in partial fulfillment of the award of the degree,

Master of Business Administration at Bangalore University, under my guidance and

supervision.

Place: Bangalore Dr. NAGESH.S.MALAVALLIDate: Professor, MPBIM,

Bangalore


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PRINCIPAL SCERTIFICATE

This is to certify that this report titled FORECASTING VOLATILITY IN OPT ION

TRADING been prepared by Ms. MADHURI ANUMALASETTY of M. P. Birla

Institute of Management in partial fulfillment of the award of the degree, Master of

Business Administration at Bangalore University, under the guidance and supervision of

Dr.NAGESH MALAVALLI, MPBIM, Bangalore.

Place: Bangalore Dr. NAGESH.S.MALAVALLIDate: (PRINCIPAL)

Bangalore


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ACKNOWLEDGMENT

I sincerely thank Dr.Nagesh. S. Malavalli (Principal), M.P.Birla Institute of Management,

Bangalore for granting me the permission to do this Research Project.

I extend my gratitude to Prof.T.V.N.Rao, and also Prof S.Santhanam, professor , MPBIM

who kindly spared their valuable time giving information without which this report

would have been incomplete.

I extend my deep sense of gratitude to my parents who have encouraged and helped me to

complete this project successfully.

I would like to extend my thanks to all the unseen hands that have made this project

possible.

Place: Bangalore

Date: MADHURI ANUMALASETTY


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SERIAL NO PARTICULARS PAGE NOABSTRACT 1

1 INTRODUCTION 2

2 LITERATURE REVIEW 10

3 RESEARCHMETHODOLOGY

16

4 FINDINGS ANDANALYSIS

23

5 CONCLUSIONS 33

6 BIBLIOGRAPHY 35

ANNEXURES 37


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CHAPTER 1

ABSTRACT


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ABSTRACT:

Options were introduced in the Indian stock markets in the year 2001(the index

options in June and individual stock options in July). There has been considerableincrease in the volumes of trading in these derivative instruments since then. 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

ten stocks and their respective options which are consistently traded during the years

2004 and 2005. The stocks are tested for stationarity and historical volatility is calculated.

Using the Black scholes option pricing model the implied volatilities are calculated.

T-test is used for find whether they are significant or not.

The findings of the study are the stock returns are stationary series and the historical and

implied volatilities are significantly different. This proved that implied volatility cannot

be forecasted only by historical volatility.


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CHAPTER 2

INTRODUCTION


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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 gold futures contract for

october 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.

EVOLUTION OF DERIVATIVES:

In the 17th century, in Japan, the rice was been grown abundantly; later the trade in rice

grew and evolved to the stage where receipts for future delivery were traded with a high

degree of standardization. This led to forward trading.

In 1730, the market received official recognition from the Tokugawa Shogunate (the

ruling clan of shoguns or feudal lords). The Dojima rice market can thus be regarded as

the first futures market, in the sense of an organized exchange with standardized trading

terms.

The first futures markets in the Western hemisphere were developed in the United States

in Chicago. These markets had started as spot markets and gradually evolved into futures

trading. This evolution occurred in stages. The first stage was the starting of agreements

to buy grain in the future at a pre-determined price with the intension of actual delivery.

Gradually these contracts became transferable and over a period of time, particularlydelivery of the physical produce. Traders found that the agreements were easier to buy

and sell if they were standardized in terms of quality of grain, market lot and place of

delivery. This is how modern futures contracts first came into being. The Chicago Board

of Trade (CBOT) which opened in 1848 is, to this day the largest futures market in the

world.


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KINDS OF FINANCIAL DERIVATIVES:

1) Forwards

2) Futures

3) Options

4) Swaps

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, the user who

promises to sell at an agreed price at a future date is said to be in short position .

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.

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.


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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.

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. The price so predetermined is called the Strike price or Exercise price .

Depending on the contract terms, an option may be exercisable on any date during a

specified period or it may be exercisable only on the final or expiration date of the period

covered by the option contract.

OPTION PREMIUM

In return for the guaranteeing the exercise of an option at its strike price, the option seller

or writer charges a premium, which the buyer usually pays upfront. Under favorable

circumstances the buyer may choose to exercise it.

Alternatively, the buyer may be allowed to sell it. If the option expires without being

exercised, the buyer receives no compensation for the premium paid.


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WRITER:

In an option contract, the seller is usually referred to as writer , since he is said to write

the contract. If an option can be excised on any date during its lifetime it is called an

American Option. However, if it can be exercised only on its expiration date, it is called

an European Option.

OPTION INSTRUMENTS:

a) Call Option

A Call Option is one, which gives the option holder the right to buy an underlying

asset at a pre-determined price.

b) Put Option

A put option is one, which gives the option holder the right to sell an und erlying

asset at a pre-determined price on or before the specified date in the future.

c) Double Option

A Double Option is one, which gives the Option holder both the right to buy or sell underlying asset at a pre-determined price on or before a specified date in the

future.

SWAPS:

A SWAP transaction is one where two or more parties exchange (swap) one pre-

determined payment for another.


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There are three main types of swaps:-

a) Interest Rate swap

b) Currency swap

c) Commodity swap

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 in

July 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 trading

volumes are very low on BSE.

The table below gives the turnover and no of contracts traded for both index options and

stock options during the years from introduction of options into Indian market. It gives

the values for both

call

and

put

options.


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Index Options Stock Options

Call Put Call Put

Month/ Year

No. of contracts

NotionalTurnover(Rs. cr.)

No. of contracts


No. of contracts


No. of contracts

NotionalTurnover

(Rs. cr.)

2001-02 113974 2466 61926 1300 768159 18780 269370 6383

2002-03 269674 5669 172567 3577 2456501 69643 1066561 30488

2003-04 1043894 31794 688520 21022 4243661 167967 1339410 49240

2004-05 1870647 69371 1422911 52572 3946979 132054 1098133 36782

STATEMENT OF THE PROBLEM:

Option pricing indicates the future expectations of the market participants.

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. So forecasting the implied volatility using the historical

volatility is the consideration of the study.


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SCOPE OF THE STUDY:

The scope of the study extends till the preview of 10 stocks and their

respective options traded consistently during the years 2004 and 2005 in National Stock

Exchange of India.

1) ACC

2) ARVINDMILLS

3) BHEL

4) DR. REDDY

5) GAIL

6) INFSYSTECH

7) ITC

8) ONGC

9) RELIANCE

10) WIPRO

OBJECTIVE OF THE STUDY:

To study the ability of forecasting the volatility by the market participants in

options trading from 2004 and 2005 using historical volatility of the underlying stocks .


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CHAPTER 3

LITERATURE REVIEW


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LITERATURE REVIEW:

The purpose if literature review is to find out the various studies that have beendone 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 and open 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 ARMA-

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

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


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The study found 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. 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 ismeasured 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., open 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 an appropriate 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 Wald s 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.

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 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


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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 sincethe introduction of options. The study finds that there is no significant change in any of

these characteristics, if one applies an appropriate 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.

Several authors have developed option-pricing formulas under alternate assumptions

about the underlying asset s 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


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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), andBeckers (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. 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.


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Data collected was of 10 stocks and their respective options for the period 2004 and

2005. Data is collected from the website NSE INDIA from F&O segment and Equity

segment.

The 10 stocks are chosen such that the respective options are traded continuously in the

period 2004 -2005.

METHODOLOGY:

To calculate the volatility of the stocks in the market, the stationarity of the time

series it to be tested. To test whether the stock returns series is random walk time seriesi.e., nonstationary stochastic process. For this UNIT ROOT TEST is calculated with a

null hypothesis that time series under consideration is nonstationary.

CALCULATION OF HISTORICAL VOLATILITY:

The daily closing prices of the individual stocks are collected. Volatility is measured by

calculating standard deviation.

Standard deviation h =sqrt [1/(n-1) (x i-X)^2 ]

Where

n=number of trading days in month

xi=ln (s i /s i-1)

si=closing stock price for i th

X=mean of x i

As this volatility is calculated using historical prices this is called Historical volatility.

CALCULATION OF IMPLIED VOLATILITY:


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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 on the first trading day of a 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 on the first trading day is considered

for the study. Risk-free interest rate is obtained from the trading information on 364-day

treasury bill yield (which can be considered as the benchmark risk-free interest rate)

published by Reserve Bank of India in its monthly bulletins.

Using this data on strike price, stock price, term to maturity and risk-free interest rate andclosing prices of call options, implied volatilities are calculated using iterative method.

BLACK SCHOLES FORMULA:

Where,

C= call premium

S=current stock price

t=time until option expiration

K=option striking price

r=risk free interest return

N=cumulative standard normal distribution

The initial value of volatility is taken as .001 and the call option price is calculated using

1 2

2

1

2 1

( ) ( )

ln( / ) ( / 2)

rt C S N d Ke N d

S K R t d

t

d d t


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Black Scholes equation and compared with market price. If the calculated option price is

less than the market price, then the volatility is increased by .001 and the call option price

is recalculated using Black scholes model and compared with the market price. This

process is continued until the calculated option price is more or less equal to market

option price. The volatility of the last iteration is taken as implied volatility.

These implied volatilities obtained on the first trading day of a month are compared with

the realized volatilities calculated for the month. To find how closely the implied and

realized volatilities are related, T test is performed.

TEST FOR STATIONARITY:

STATIONARY STOCHASTIC PROCESS:

A random or stochastic process is a collection of random variables ordered in time .A

stochastic process is said to be stationary if its mean and variance are constant over time

and the value of the covariance between the two time periods depends only on the

distance or gap or lag between the two time periods and the actual time at which the

covariance is computed.

NON STATIONARY STOCHASTIC PROCESS:

A stochastic process is said to be non stationary if its mean and variance change over

time. An example for non stationary is random walk model.

There are two types of random walk:

Random walk without drift

Random with drift


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RANDOM WALK WITHOUT DRIFT:

The series Y t is said to be random walk without drift if,

Y t=Y (t-1) +U t

This .shows, the value of Y at time t is equal to its value at time(t-1) plus random shock

.U t is a white noise error term with mean 0 and variance 2

RANDOM WALK WITH DRIFT:

The series Y t is said to be random walk with drift if,

Y t=Y (t-1) +U t +

Where is known as the drift parameter .The series Y t drifts upward or downward,

depending on being positive or negative.

In this study, random walk without drift is considered.i.e.,

Y t=Y (t-1) +U t

UNIT ROOT TEST:

A test of stationarity (or nonstationarity) that is well known is the UNIT ROOT TEST.

The starting point of unit root test is

Y t= Y (t-1) +U t

Where,

Ut=white noise term.

Y t= random variable at discrete time interval t.


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If =1, then the unit root exist. That is: the time series under consideration is

nonstationary or follows a random walk.

If ! = 1, then unit root does not exist. That is: the time series under consideration isstationary.

Theoretically value can be c alculated by regressing Y t with one period lag values.

AUGMENTED DICKEY FULLER (ADF) TEST:

ADF Test is used for calculating , where = -1.

Hypothesis:

H0= Time series is non stationary.

If = 0.(unit root)

H1= Time series is stationary.

If ! =0.

Decision Rule:

1) If T*>ADF critical value not reject the null hypothesis i.e., unit root exists.

2) If T*


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T-Test for the significance of an observed sample correlation coefficient.

T-Test for Difference Of Means:

This test is conducted to find the relationship between historical and implied

volatilities.

Hypothesis:

Null hypothesis H 0 = sample mean does not differ significantly. (T calT tab)


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CHAPTER 5

DATA INTERPRETATION AND ANALYSIS


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ADF TEST

This test is conducted using the log returns of the ten stocks and EVIEW software and the

results are tabulated as follows.

TABLE: ADF TEST TAU VALUES

NAME OF THE STOCK TAU STATISTIC VALUE

1) ACC

2) ARVINDMILLS

3) BHEL

4) DRREDDY

5) GAIL

6) INFSYSTECH

7) ITC

8) ONGC

9) RELIANCE

10) WIPRO

-22.18684

-19.05888

-20.93857

-21.63807

-21.82448

-22.28470

-21.64007

-20.37510

-21.4420

-23.05502


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TABLE: ADF TEST TAU VALUES

The table below gives the ADF test critical values at various significance levels.

TABLE: CRITICAL VALUES OF ADF TEST

SIGNIFICANCE LEVEL CRITICAL VALUE

1%

5%

10%

-2.5699

-1.9401

-1.6160

INTERPRETATION:

From the above two tables it is observed that TAU statistic value is lesser than the critical

values at various significance levels. This shows that null hypothesis gets rejected i.e., the

series is under consideration is stationary.


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TABLE: HISTORICAL VOLATILITY FOR INFSYSTECH, ITC, ONGC,

RELIANCE, WIPRO

YEARS INFSYSTECH ITC ONGC RELIANCE WIPRO

Jan-04 0.024650271 0.025825992 0.048468814 0.0237071 0.024131

Feb-04 0.020915115 0.017906567 0.028488779 0.0203246 0.023149

Mar-04 0.024744349 0.011181726 0.025755899 0.0180703 0.020983

Apr-04 0.024506622 0.008574053 0.017527346 0.0178594 0.028573

May-04 0.041019415 0.039178954 0.054711006 0.04918 0.075652

Jun-04 0.014435691 0.012276898 0.022569819 0.0239434 0.239754

Jul-04 0.015089829 0.024912438 0.026880897 0.0187511 0.017103

Aug-04 0.012407528 0.014499606 0.015004315 0.0156245 0.019967

Sep-04 0.013805744 0.016289484 0.012714018 0.0131225 0.014928

Oct-04 0.020752451 0.007553094 0.013320418 0.0164469 0.019585

Nov-04 0.014179954 0.016590817 0.012256669 0.0144797 0.013061

Dec-04 0.011076854 0.011634555 0.012262192 0.0189432 0.011663

Jan-05 0.02094495 0.029494756 0.014141157 0.0153786 0.025595

Feb-05 0.014341689 0.0088987 0.010505545 0.0117772 0.015582

Mar-05 0.013335186 0.017145153 0.019567884 0.0169448 0.02098

Apr-05 0.021547688 0.013364775 0.016501966 0.0176958 0.026904

May-05 0.014938904 0.011180737 0.012205583 0.0112019 0.015975

Jun-05 0.016051574 0.014809089 0.013815019 0.0186077 0.012415

Jul-05 0.01939999 0.013550613 0.017626971 0.0179277 0.014614

Aug-05 0.014190727 0.011216931 0.015804421 0.018336 0.15072

Sep-05 0.014715224 0.587563989 0.016794302 0.0167356 0.017062

Oct-05 0.019000952 0.023499993 0.018510607 0.0154717 0.025734

Nov-05 0.013743842 0.01983605 0.014057737 0.0105073 0.021298

Dec-05 0.013081762 0.016813532 0.016723901 0.0134493 0.021298


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TABLE: IMPLIED VOLTAITY FOR ACC, ARVIND

MILLS,BHEL,DRREDDY,GAIL

YEARS ACC ARVINDMILLS BHEL DRREDDY GAIL

Jan-04 0.4852 0.642 0.4298 0.3573 0.5685

Feb-04 0.508 0.89 0.3756 0.4185 0.4966

Mar-04 0.3721 0.842 0.3157 0.5084 0.3905

Apr-04 0.3315 0.581 0.448 0.4033 0.324

May-04 0.0615 0.741 0.4945 0.3613 0.3579

Jun-04 0.358 0.82 0.2642 0.4149 0.5185

Jul-04 0.326 0.701 0.2634 0.3473 0.474

Aug-04 0.2037 0.57 0.2192 0.7857 0.3955

Sep-04 0.281 0.5243 0.2692 0.2734 0.2347

Oct-04 0.4385 0.463 0.2543 0.3102 0.402

Nov-04 0.3965 0.499 0.2838 0.295 0.2825

Dec-04 0.349 0.645 0.2345 0.3352 0.31

Jan-05 0.3859 0.6101 0.2495 0.3468 0.395

Feb-05 0.2043 0.525 0.2451 0.3478 0.2982

Mar-05 0.2645 0.475 0.2503 0.2618 0.3394

Apr-05 0.2772 0.591 0.1528 0.3359 0.3783

May-05 0.1812 0.518 0.1806 0.365 0.2843

Jun-05 0.2037 0.37 0.2529 0.1451 0.282

Jul-05 0.3343 0.4701 0.3305 0.1936 0.2812

Aug-05 0.385 0.5425 0.3091 0.3275 0.334

Sep-05 0.2242 0.4765 0.2344 0.3105 0.1957

Oct-05 0.2685 0.513 0.2278 0.2338 0.3349

Nov-05 0.2138 0.4245 0.2134 0.2259 0.3139

Dec-05 0.4163 0.412 0.1546 0.1661 0.346


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TABLE: IMPLIED VOLATILITY FOR

INFSYSTECH,ITC,ONGC,RELIANCE,WIPRO

YEARS INFSYSTECH ITC ONGC RELIANCE WIPRO

Jan-04 0.4446 0.3908 0.4689 0.3675 0.4518

Feb-04 0.32378 0.3164 0.4723 0.3447 0.4169

Mar-04 0.28624 0.6825 0.2117 0.2878 0.3625

Apr-04 0.3749 0.2035 0.2103 0.2564 0.3716

May-04 0.26624 0.136 0.3078 0.3445 0.2949

Jun-04 0.2712 0.239 0.4245 0.3687 0.3144

Jul-04 0.2988 0.2498 0.3033 0.368 0.2961

Aug-04 0.2233 0.2275 0.2513 0.279 0.3472

Sep-04 0.1809 0.2293 0.0768 0.22 0.2456

Oct-04 0.2434 0.2709 0.2428 0.2473 0.3285

Nov-04 0.2018 0.2202 0.2274 0.277 0.2849

Dec-04 0.243 0.2092 0.19 0.306 0.2315

Jan-05 0.2876 0.2596 0.2747 0.3155 0.3106

Feb-05 0.2545 0.2476 0.1882 0.2352 0.294

Mar-05 0.2386 0.2113 0.1375 0.2442 0.2825

Apr-05 0.265 0.2095 0.2411 0.3052 0.3009

May-05 0.247 0.1942 0.1994 0.2075 0.2345

Jun-05 0.2101 0.199 0.1774 0.2594 0.2563

Jul-05 0.2647 0.1273 0.2895 0.3062 0.267

Aug-05 0.2595 0.2484 0.2422 0.3206 0.275

Sep-05 0.1855 0.2292 0.1322 0.2422 0.2775

Oct-05 0.3391 0.3715 0.2738 0.3304 0.3777

Nov-05 0.2079 0.2335 0.2454 0.181 0.2975

Dec-05 0.2 0.277 0.2187 0.2554 0.728


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T TEST :

T-Test is conducted for historical and implied volatility to test whether they are

significantly different or not.

TABLE: T CALCULATED VALUES

NAME T (CALCULATED)

1) ACC

2) ARVINDMILLS

3) BHEL

4) DRREDDY

5) GAIL

6) INFSYSTECH

7) ITC

8) ONGC

9) RELIANCE

10) WIPRO

17.65671

10.10587

18.69865

15.92438

16.00968

21.78401

15.92438

20.82507

20.54226

15.66004


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INTERPRETATION:

T tabulated value for 23 degrees of freedom is 1.96.From the values in the above tabularcolumn it is shown that (T cal>T tab). Hypothesis is rejected that is the two sample mean

differ significantly.


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CHAPTER 5

CONCLUSION


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CONCLUSION:

The market future volatility cannot be used as an estimate for the implied volatility.The

ability of forecasting the implied volatility by market participants cannot be estimatedusing only historical volatility of stock returns because the T test conducted proves that

the two sample means differ significantly. So no relation can be proved existing between

the historical volatility and implied volatility.

Probably use of more sophisticated methods like GARCH would have given better results

in estimating the volatilities


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CHAPTER 6

BIBLIOGRAPHY


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TEXT BOOKS REFERRED

INVESTMENT ANALYSIS AND PORTFOLIO MANAGEMENT BY PRASANNA CHANDRA

BASIC ECONOMETRICS DAMAODARAN GUJARATI

JOURNALS REFERRED

ICFAI JOURNAL ON APPLIED FINANCE

OTHER ARTICLES REFERRED

Paper1:

Index Futures Trading and Spot Market Volatility:Evidence from an

Emerging Market

Paper 2:

The Impact of Option Introduction on the olatility of an Underlying

Stock of a Company:The Indian Case

Paper 3:

OPTION VALUES UNDER STOCHASTIC VOLATILITY heory

and Empirical Estimates

WEBSITES REFERRED

www.google.com

www.nseindia.com
http://www.nseindia.com/http://www.google.com/


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