Upload
panchaksharimb
View
218
Download
0
Embed Size (px)
Citation preview
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
1/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 1
FORECASTING VOLATILITY IN OPTION TRADING
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)
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
2/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 2
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
3/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 3
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
4/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 4
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
5/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 5
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
6/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 6
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
7/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 7
CHAPTER 1
ABSTRACT
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
8/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 8
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
9/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 9
CHAPTER 2
INTRODUCTION
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
10/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 10
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
11/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 11
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
12/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 12
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
13/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 13
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
14/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 14
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
15/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 15
Index Options Stock Options
Call Put Call Put
Month/ Year
No. of contracts
NotionalTurnover(Rs. cr.)
No. of contracts
NotionalTurnover(Rs. cr.)
No. of contracts
NotionalTurnover(Rs. cr.)
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
16/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 16
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 .
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
17/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 17
CHAPTER 3
LITERATURE REVIEW
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
18/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 18
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
19/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 19
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
20/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 20
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
21/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 21
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
22/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 22
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
23/43
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
24/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 24
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:
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
25/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 25
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
26/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 26
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
27/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 27
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
28/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 28
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*
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
29/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 29
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)
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
30/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 30
CHAPTER 5
DATA INTERPRETATION AND ANALYSIS
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
31/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 31
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
32/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 32
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
33/43
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
34/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 34
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
35/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 35
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
36/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 36
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
37/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 37
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
38/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 38
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.
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
39/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 39
CHAPTER 5
CONCLUSION
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
40/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 40
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
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
41/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 41
CHAPTER 6
BIBLIOGRAPHY
8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
42/43
FORECASTING VOLATILITY IN OPTION TRADING
M. P BIRLA INSTITUTE OF MANAGEMENT 42
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/8/7/2019 For Casting Volatility in Option Trading-Madhuri Anumalshetty-0425
43/43
FORECASTING VOLATILITY IN OPTION TRADING
www.icfaipress.com
ANNEXURES
http://www.icfaipress.com/