Download Derivatives Trading and Its Impact on the Volatility of NSE, India

Derivatives Trading and Its Impact on the
Volatility of NSE, India
GEL : G10, G14, G20, G19
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ABSTRACT
This article examines the impact of introduction of financial derivatives trading on the
volatility of Indian stock market (an emerging stock market). It examines the theme that the
introduction of derivatives in the stock market in India would reduce the volatility (risk) in the
stock market. NSE Nifty 50 index has been used as a proxy of stock market return.
ARCH/GARCH technique has been employed in the analysis. The conditional volatility of
interday market returns before and after the introduction of derivatives products are estimated
with the (GARCH) model. The Finding suggests that derivatives trading has reduced the
volatility.
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Executive Summary
Derivatives trading in the stock market have been a subject of enthusiasm of research in the
field of finance the most desired instruments that allow market participants to manage risk in the
modern securities trading are known as derivatives. The derivatives are defined as the future
contracts whose value depends upon the underlying assets. If derivatives are introduced in the
stock market, the underlying asset may be anything as component of stock market like, stock
prices or market indices, interest rates, etc. The main logic behind derivatives trading is that
derivatives reduce the risk by providing an additional channel to invest with lower trading cost
and it facilitates the investors to extend their settlement through the future contracts. It provides
extra liquidity in the stock market.
In recent past, the volatility of stock returns has been a major topic in finance literature.
Generally, volatility is considered as a measurement of risk in the stock market return and a lot of
discussions have taken place about the nature of stock return volatility. Therefore, understanding
factors that affect stock return volatility is an imperative task in many ways. Stock prices and
their volatility add to the concern of attention in the stock market, especially in India. The
volatility on the stock exchanges may be thought of as having two components: The volatility
arising due to information based price changes and Volatility arising due to noise trading/
speculative trading, i.e., destabilizing volatility. As a concept, volatility is simple and intuitive.
Derivatives’ trading has been started in Indian stock market with the theme that it would reduce
the Volatility. Empirical researchers have tried to find a pattern in stock return movements or
factors determining these movements. Nath (2003) Shenbagaraman (2003) Mayhew (2000) Raju
and Karande (2003) Rahman (2001) have examined empirically the impact of derivatives trading
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on the spot market volatility. The majority of studies have employed the standard ARCH or
GARCH model to examine volatility shifting. Mostly the findings are supporting the hypothesis
that introduction of derivatives has reduced the stock market volatility. In the case of Indian
stock market, the results are the same, but the studies are based on the shorter period.
Extending the studies, this research article examines the impact of introduction of
financial derivatives on cash/spot market volatility in Indian stock market (an emerging stock
market) using a larger period as well as It examines the impact of trading in major derivatives
products including index futures, stock futures and index options on the conditional volatility of
stock market return and makes an effort to study whether the volatility in the Indian stock
markets has undergone any significant change after the introduction of derivatives trading. NSE
Nifty 50 index has been used as a proxy for stock market return for the period of June 2000 to
June 2006. The result is supporting the theme, in general, that derivatives trading have reduced
the volatility of Indian stock market.
Kew Words: Financial derivatives, Volatility, spot market, efficiency, risk
management.
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1 - INTRODUCTION
The global liberalisation and integration of financial markets has created new
investment opportunities, which in turn require the development of new instruments that are
more efficient to deal with the increased risks. Institutional investors who are actively engaged in
industrial and emerging markets need to hedge their risks from these internal as well as crossborder transactions.
Agents in liberalised market economies who are exposed to volatile
commodity price and interest rate changes require appropriate hedging products to deal with
them. And the economic expansion in emerging economies demands that corporations find better
ways to manage financial and commodity risks.
The most desired instruments that allow market participants to manage risk in the
modern securities trading are known as derivatives. The main logic behind the derivatives
trading is that derivatives reduce the risk by providing an additional channel to invest with lower
trading cost and it facilitates the investors to extend their settlement through the future contracts.
It provides extra liquidity in the stock market. They represent contracts whose payoff at
expiration is determined by the price of the underlying asset—a currency, an interest rate, a
commodity, or a stock.
Derivatives are traded in organized stock exchanges or over the counter by derivatives
dealers. The issue of the impact of derivatives trading on stock market volatility has received
considerable attention in recent years in India, particularly after the stock market crash of 2001.
Derivative products like futures and options on Indian stock markets have become important
instruments of price discovery, portfolio diversification and risk hedging in recent times. In the
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last decade, many emerging and transition economies have started introducing derivative
contracts.
The history of derivatives may be new for developing countries but it is old for the
developed countries. The history of derivatives is surprisingly longer than what most people
think. The derivatives contracts were done not formally in the old times in the informal sectors.
The advent of modern day derivative contracts is attributed to the need for farmers to protect
themselves from any decline in the price of their crops due to delayed monsoon, or
overproduction.
The first derivative as 'futures' contracts were introduced in the Yodoya rice market in
Osaka, Japan around 1650. The contracts were evidently standardised contracts, like today's
futures. The commodity derivative market has been functioning in India since the nineteenth
century with organized trading in cotton through the establishment of Cotton Trade Association
in 1875. Exchange traded financial derivatives were introduced in India since June 2000 at the
two major stock exchanges, NSE and BSE. There are various contracts (Index futures, Stock
futures, Index options, Stock options, interest rate futures, currency options) currently traded on
these exchanges. (Shenbagaraman 2003).
1.1 - Role of Financial Derivatives
Derivatives may be traded for a variety of reasons. Derivatives enable a trader to hedge
some pre-existing risk by taking positions in derivatives markets that offset potential losses in the
underlying or spot market. In India, most derivatives users describe themselves as hedgers and
Indian laws generally require that derivatives be used for hedging purposes only. Another motive
for derivatives trading is speculation (i.e. taking positions to profit from anticipated price
movements). In practice, it may be difficult to distinguish whether a particular trade was for
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hedging or speculation, and active markets require the participation of both hedgers and
speculators.
It is argued that derivatives encourage speculation, which destabilizes the spot market.
The alleged destabilization takes the form of higher stock market volatility. The reason behind it
is informational effect of the futures trading. Futures trading can alter the available information
for two reasons: first, futures trading attract additional traders in the market; second, as
transaction costs in the futures market are lower than those in the spot market, new information
may be transmitted to the futures market more quickly. Thus, future markets provide an
additional route by which information can be transmitted to the spot markets and therefore,
increased spot market volatility may simply be a consequence of the more frequent arrival and
more rapid processing of information.
Raju and Ghosh (2004) have expressed view for the consideration of volatility in the Indian
stock market as tools of analysis of risk factors. Stock prices and their volatility add to the
concern of attention. The growing linkages of national markets in currency, commodity and stock
with world markets and existence of common players, have given volatility a new property – that
of its speedy transmissibility across markets.
Among the general public, the term volatility is simply synonymous with risk. In their view,
high volatility is to be deplored, because it means that security values are not dependable and the
capital markets are not functioning as well as they should. Merton Miller (1991) the winner of the
1990 Nobel Prize in economics - writes in his book "Financial Innovation and Market Volatility"
…. “By volatility public seems to mean days when large market movements, particularly down
moves, occur. These precipitous market wide price drops cannot always be traced to a specific
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news event.... The public takes a more deterministic view of stock prices; if the market crashes,
there must be a specific reason.” (Cited in Raju and Ghosh 2004).
The volatility on the Indian stock exchanges may be thought of as having two components:
The volatility arising due to information based price changes and Volatility arising due to noise
trading/ speculative trading, i.e., destabilizing volatility. As a concept, volatility is simple and
intuitive.
In a large scale, the success of derivatives trading will depend on the choice of products to
be traded in the markets. The popularly traded and usual types of derivatives are futures and
options. The products to be traded in the stock markets need to have the following characteristics
which are mentioned by Tsetsekos Varangis (2000):
......a sufficiently higher as well as lower level of price volatility to attract hedgers or
speculators, a significant amount of money for speculative motive at a certain level of risk; a
significant number of domestic market participants—and possibly buyers and sellers from
abroad; a large number of producers, processors, and banks interested in using derivatives
contracts (that is, enough speculators to provide additional liquidity); and a weak correlation
between the price of the underlying asset and the price of the already-traded derivatives
contract(s) in other exchanges (basis risk).
Introduction of derivatives in the Indian capital market was initiated by the Government
following L C Gupta Committee Report on Derivatives in December 1997. The report suggested
the introduction of stock index futures in the first place to be followed by other products once the
market matures. Following the recommendations and pursuing the integration policy, futures on
benchmark indices (Sensex and Nifty 50) were introduced in June 2000. The policy was followed
by introduction of index options on indices in June 2001, followed by options on individual
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stocks in July 2001. Stock futures were introduced on individual stocks in November, 2001 (Nath
2003)
By definition, derivatives are the future contracts whose value depends upon the underlying
assets. When derivatives are introduced in the stock market, the underlying asset may be anything
as component of stock market like, stock prices or market indices, interest rates, etc. Derivatives
products are specialised contracts* which signify an agreement or an option to buy or sell the
underlying asset to extend up to the maturity time in the future at a prearranged price.
Only futures and options are used in this analysis, so these are introduced in brief.
Futures: A futures contract is an agreement between two parties to buy or sell an asset at a
certain time in the future at a certain price. Presently Index futures on S&P CNX NIFTY and
CNX IT, Stock futures on certain specified Securities and Interest Rate Futures are available for
trading at NSE. All the futures contracts are settled in cash. A futures contract is a forward
contract which trades on an exchange. Futures markets feature a series of innovations in how
trading is organised. (Shah Thomas 2000)
Options: An Option is a contract which gives the right, but not an obligation, to buy or sell the
underlying at a stated date and at a stated price. While a buyer of an option pays the premium
and buys the right to exercise his option, the writer of an option is the one who receives the
option premium and therefore obliged to sell/buy the asset if the buyer exercises it on him.
The above description about the derivatives creates a research problem that need be
reported. What is the impact of derivatives trading on the stock market risk and return in
practice? The theoretical literature on derivatives trading is of the view that derivatives trading
*
The contract has a fixed expiry period mostly in the range of 3 to 12 months from the date of commencement of
the contract. The value of the contract depends on the expiry period and also on the price of the underlying asset
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increase the efficiency of the stock market through minimising the risk, but the opposite effect
may also be caused by derivatives trading.
The rest of the paper is organised as follows: First, some relevant and related literatures
have been reviewed. Thereafter the methodology, data and the time period for the study have
been explained. The variables are identified and explained in brief. Then the models have been
specified and estimated. The interpretations of the results are presented along with the result
tables. The findings are presented as conclusion.
2 - Theoretical foundations and Review of literature.
Derivatives trading in the stock market have been a subject of enthusiasm of research in
the field of finance. Derivatives trading have two attributes on the basis of its effectiveness. So
there have often been contrary views among the researchers of what may be the impact of
derivatives trading. According to the nature of this instrument it is argued that this could enhance
the market efficiency by establishing the market. There are many empirical findings for both
there roles of derivatives trading. Here some review of literature for both these results are
presented.
Many theories have been developed about the pros and cons of the impact of derivatives
trading in the stock market. A common agreement has been found among the studies that the
introduction of derivatives products, specially the equity index futures enables traders to transact
large volumes at much lower transaction costs relative to the cash market.
A major theoretical argument for the benefit of derivatives trading is that it reduces the
volatility of the stock market. The logic is that it reduces the asymmetric information among the
investors and information reduces the speculation in the trading system. A variety of theoretical
arguments have been advanced over the years to explain why speculative trading in general, or
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the existence of derivatives markets in particular, might affect the volatility of the underlying
asset market.
In recent past, the volatility of stock returns has been a major topic in finance literature.
Empirical researchers have tried to find a pattern in stock return movements or factors
determining these movements. Generally, volatility is considered as a measurement of risk in the
stock market return and a lot of discussions have taken place about the nature of stock return
volatility. Therefore, understanding factors that affect stock return volatility is an imperative task
in many ways.
A numbers of theoretical and empirical studies have been done on the impact of the
introduction of derivatives in the stock markets on the stock return volatility. The studies are
concerned with both the developed as well as developing countries. There are two sets of views
according to the theoretical as well as empirical findings. One is of the view that introduction of
derivatives has increased the volatility and market performance, through forwarding its
speculative roles and the other view is that the introduction of derivatives has reduced the
volatility in the stock market thus increasing the stability of the stock market.
The behaviour of volatility in the equity market in India, for the pre and post derivatives
period, has been examined using conditional variance for the period of 1999-2003 in (Nath,
2003). He modeled conditional volatility using different method such as GARCH (1,1). He has
considered 20 stocks randomly from the Nifty and Junior Nifty basket as well as benchmark
indices itself. As result, he observed that for most of the stocks, the volatility came down in the
post-derivative trading period. All these methods suggest that the volatility of the market as
measured by benchmark indices like S&P CNX Nifty and Nifty Junior have fallen in the postderivatives period.
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The impacts of the introduction of the derivatives contracts such as Nifty futures and
options contracts on the underlying spot market volatility have been examined using a model that
captures the heteroskedasticity in returns that is recognised as the Generalised Auto Regressive
Conditional Heteroskedasticity (GARCH) Model in Shenbagaraman (2003). She used the daily
closing prices for the period 5th Oct. 1995 to 31st Dec. 2002 for the CNX Nifty the Nifty Junior
and S&P500 returns. Results indicate that derivatives introduction has had no significant impact
on spot market volatility but the nature of the GARCH process has changed after the introduction
of the futures trading.
Both theoretical and empirical aspect of the question of how the speculation, in general,
and derivative securities in particular, effects the underlying asset markets has been explained in
Mayhew (2000). The theoretical research has revealed that there are many different aspects of
the relationship between cash and derivative markets. Although many models predict that
derivatives should have a stabilizing effect, this result normally requires restrictive assumptions.
At the end of the day, the theoretical literature gives ambiguous predictions about the effects of
derivatives markets.
Price discovery and volatility have been examined in the context of introduction of Nifty
futures at the National Stock Exchange (NSE) in June 2000 applying Cointegration and
Generalised Auto Regressive Conditional Heteroscedasticity (GARCH) techniques respectively
from January1998 to October 2002 in Raju and Karande (2003). Their finding suggests that the
introduction of futures has reduced volatility in the cash market.
The impact of trading in the Dow Jones Industrial Average index futures and futures
options on the conditional volatility of component stocks has been examined in Rahman (2001).
The conditional volatility of intraday returns for each stock before and after the introduction of
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derivatives is estimated with the GARCH model. Estimated parameters of conditional volatility
in pre-futures and post-futures periods are then compared to determine if the estimated
parameters have changed significantly after the introduction of various derivatives. The data for
this study consist of transaction prices from the 30 stocks comprising the DJIA. Transaction
prices for April through June 1997 (pre-futures period) and April through June 1998 (postfutures period) are used. The results suggest that the introduction of index futures and options on
the DJIA has produced no structural changes in the conditional volatility of component stocks.
The null hypothesis of no change in conditional volatility from pre futures to post futures periods
cannot be rejected.
Gupta (2002) has examined the impact of index futures introduction on stock market
volatility. Further, he has also examined the relative volatility of spot market and futures market.
He has used daily price data (high, low, open and close) for BSE Sensex and S&P CNX Nifty
Index from June 1998 to June 2002. Similar data from June 9, 2000 to March 31, 2002 have also
been used for BSE Index Futures and from June 12, 2000 to June 30, 2002 for the Nifty Index
Futures. He has used four measures of volatility the first is based upon close-to-close prices, the
second is based upon open-to-open prices, the third is Parkinson’s Extreme Value Estimator, and
the fourth is Garman-Klass measure volatility (GKV). The empirical results indicate that the
over-all volatility of the underlying stock market has declined after the introduction of index
futures on both the indices.
The impact of the introduction of index futures on the volatility of stock market in India
was examined employing daily data of Sensex and Nifty CNX for period of Jan 1997-March
2003 in Bandivadekar and Ghosh (2005). The return volatility has been modeled using GARCH
framework. They found strong relationship between information of introduction of derivatives
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and return volatility. They have concluded that the introduction of derivatives has reduced the
volatility of the stock market. The same study was done by Hetamsaria and Swain (2003). they
have examined the impact of the introduction of index futures on the volatility of stock market in
India applying regression analysis. They have used Nifty 50 index price data for the period of
Jan 1998 - March 2003. They found that the volatility of the Nifty return has declined after the
introduction of index futures.
Darrat, Rahman, and Zhong (2002) have examined the impact of the introduction of
index futures on the volatility of stock market in India and causal relationship between volume in
the futures market and spot market. They have used EGARCH approach and Granger Causality
(G C) test. Their finding suggests that index futures trading may not be blamed for the increasing
volatility in the spot market. They found that volatility in the spot market has produced volatility
in the futures market.
Board, Sandamann and Sutcliffe (2001), have tested the hypothesis that increases in the
futures market trading activity increases spot market price volatility. They used the GARCH
model and Schewert Model and found that the result does not support the hypothesis. The data
samples are taken from the U K market. Jeanneau and Micu (2003) have explained that
information based or speculative transaction also creates a link between volatility and activity in
asset and derivatives market. This link depends in part on whether the new information is private
or public and on the type of asset traded. In theory, the arrival of new private information should
be reflected in a rise in the volatility of return and trading volumes in single equity and equity
related futures and options.
The majority of studies have employed the standard ARCH or GARCH model to
examine volatility shifting. Mostly the findings are supporting the hypothesis that introduction of
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derivatives has reduced the market volatility. These studies use daily observations to estimate
volatility, whereas interday data are used here. Given that financial markets display high speeds
of adjustment, studies based on longer intervals such as daily observations may fail to capture
information contained in intraday market movements. Moreover, because of modern
communications systems and improved technology, volatility measures based on daily
observations ignore critical information concerning intraday price patterns. Andersen (1996)
pointed out that the focus of the market microstructure literature is on intraday patterns rather
than interday dynamics.
This study is also based on the hypothesis that the introduction of the derivatives products
has reduced the risk inefficiency in the BSE stock market. Three derivatives products (index
futures, stock futures and index options) have been used that have been introduced in the
different time periods. The time period is also for about 8 years including the most recent earning
period as 2005-2006. Derivatives turnover also have been used for the same return series.
3 - Objective of the Study
The introduction of equity index derivative contracts in Indian market has not been very
old but today the total notional trading values in derivatives contracts are ahead of cash market.
Given such dramatic changes, the objective of this study is to study the behaviour of volatility in
cash market after the introduction of derivatives contracts. This is to examine with help of
econometric model whether the introduction of derivative contracts has reduced the risk and
inefficiency in the Indian stock market or not.
4 - Hypothesis
One view is that derivatives trading increases volatility in the spot market due to more
highly leveraged and speculative participants in the futures market. An alternative view is that
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derivatives trading reduce spot market volatility by providing low cost contingent strategies and
enabling investors to minimize portfolio risk by transferring speculators from spot markets to
futures markets. So, for all the models, the null hypothesis (H0) is that the introduction of the
derivatives products has not reduced the volatility of spot market (NSE). The alternative
hypothesis (Halt) is that H 0 has been rejected.
5 - Methodology
The Autoregressive Conditional Heteroskedasticity (ARCH) and Generalized ARCH
(GARCH) models have been employed to estimate the conditional volatility of stock market
returns and the impact of the derivatives trading. GARCH model is used to test the informational
effect on the conditional volatility of stock market return.
Stock market return is calculated from the daily closing prices of the NSE stock index S&P
CNX Nifty 50. This is one of the most important and popular indicators of the Indian stock
market performance of two national indices namely Sensex, having 30 blue chip companies’
shares in the BSE and Nifty 50. These Indices are a good predictor of the stock market volatility.
Initially, derivatives were introduced only in the two major indices, Sensex and Nifty 50. Even at
present these two indices are the primes as underlying for derivatives trading in India. CNX Nifty
50 has been used in the analysis as the proxy of stock market return and it would help to
understand the impact on the functioning of the stock market.
Along with CNX Nifty 50 on which derivative products are available, we also consider
the impact of return in Nifty Junior, on which derivative products have not been introduced
(within the time period 1998-2006). The reason is to know whether the derivatives products are
the only factors affecting the market volatility or there are some others factors also. A
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comparison of fluctuations in volatility between Nifty Junior and Nifty 50 may provide a clue to
segregate the fluctuations due to introduction of future products and due to other market factors.
We have measured the informational impact of the derivative trading. We have tried to see
whether the information of the introduction of derivatives as risk controller has any impact on the
risk factor of the stock market.
Both the major derivatives products as futures and options have been considered. In
futures, we have selected index futures and stock futures. In options, we have selected index
options. The main aim of this study is only to examine the impact of derivatives for different
period of time, so these derivatives products are used only for the division of different time
periods. So, one should not be confused that why individual stocks for stock index futures have
not been used.
Dummy variables for these derivatives products (index futures, stock futures and index
options) are used as independent variables. Both the futures and options are actively traded in the
Indian stock market (NSE). The series have been created using ‘0’ for pre-derivatives
introduction period and ‘1’ for post-derivatives introduction period to get a time series as usual
used by the experts. If the coefficient on the dummy variable is statistically significant, the
introduction of has a significant impact on the spot market volatility. To address the second issue,
we divided the sample into the pre-derivatives and post- derivatives sub-sample and a GARCH
model is estimated separately for each sub-sample. Estimated parameters of conditional volatility
in pre-derivatives and post-derivatives periods are then compared to determine if the estimated
parameters have changed significantly after the introduction of derivatives. Prices in the cash
market and futures/options market are expected to be inter-related.
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The analysis is based on daily time series data. Data for the stock indices (Nifty 50,
Nifty Junior and S&P 500) has been used for the period of January 1998 to June 2006. The
closing prices in the end of the day have been used. The whole time period is divided into two
sub-time periods. First is pre-derivatives introduction period that is from Jan 1998 to June 2000
for index futures, Jan 1998 Dec 2000 for stock futures and from Jan 1998 to June 2001 for index
options. Second sub-time period is post-derivatives period from the above categorizations to June
2006. The data sources are the official websites of the NSE, SEBI and Yahoo finance.com.
The index futures are popular among the investors and this is the most actively trading
instrument in the derivatives products. Second important product is stock futures that were
introduced after the introduction of index futures. There was a big artificial fluctuation in the
stock market in 2001 because of stock market scam. The stock futures are introduced after the
scam. This is why we have used the period of introduction of stock futures also. Options are also
introduced in June 2001 following a forward step towards derivatives trading, so we have tested
the options also.
Table 1:- Date of Introduction of Derivatives Products
Der. Products
Date of Intro.
Underlying Ind.
Index Futures
June 2000
Sensex, S& P Nifty
Stock Futures
Dec. 2001
Sensex, S& P Nifty
Index Options
June 2001
Sensex, S& P Nifty
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The derivatives’ trading is not the only one factor affecting the stock market volatility
(risk), there may be other factors also. It is important to remove market-wide influences on
market return, if we are to isolate the impact of futures introduction. In order to do this we need a
proxy that is not associated with any futures/options contract, and yet captures market-wide
influences in India. For example, information news releases relating to economic conditions like,
inflation rates, growth forecasts, exchange rates, etc are likely to affect the whole market.
It is necessary to remove the effects for all these factors on price volatility. Since the
Nifty Junior has no futures/options contracts traded on it (till June 2006), we use it as a proxy to
capture market-wide information effects and to study the market wide factors contributing to the
changes in spot market volatility index as independent variable affecting the stock market return.
Return series of S&P500 index (an USA stock market index) has been used as a proxy of the
worldwide factors affecting stock market volatility.
5.1 - The GARCH Model
The GARCH model was developed by Bollerslev (1986) as a generalised version of Engle’s
(1982) Autoregressive Conditional Heteroscedasticity (ARCH). In the GARCH model the
conditional variance at time ‘t’ depends on the past values of the squared error terms and the past
conditional variances. It uses the past disturbances to model the variance of the series and allows
the variance of error term to vary over time.
Bollerslev (1986) generalized the ARCH process by allowing the conditional variance to
be a function of prior period's squared errors as well as its past conditional variance. The
advantage of a GARCH model is that it captures the tendency in financial time series data for
volatility clustering. It therefore enables us to make the connection between information and
volatility explicit, since any change in the rate of information arrival to the market will change
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the volatility in the market. Thus, unless information remains constant, which is hardly the case,
volatility must be time varying, even on a daily basis.
A model with errors that follow a GARCH (1,1) process is represented as follows:
Yt
=
a + b1Xt + Ut
...1
ht
=
a + b1(Ut-1)2 + b2ht-1
...2
Where,
ht
=
conditional variance (sigma square)
Ut
=
Error term
Equation '1' is called the conditional mean equation and equation '2' is called the conditional
variance equation. The coefficient of the error square term can be viewed as a “news”
coefficient, with a higher value implying that recent news has a greater impact on price changes.
It can be predicted as the impact of yesterday’s (the previous time period) news on today’s
(present time period) price changes. The coefficient of the variance (ht-1) reflects the impact of
“old news', in other words it is picking up the impact of prior news on yesterdays variance and as
such indicated the level of persistence in the information effect on volatility.
This estimation technique enables us to explore the link between information/news
arrival in the market and its effect on cash market volatility. Estimated parameters of conditional
volatility in pre-futures and post-futures periods are then compared to determine if the estimated
parameters have changed significantly after the introduction of the futures.
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The GARCH (1,1) framework has been extensively found to be most parsimonious
representation of conditional variance that best fits many financial time series (Bollerslev, 1986;
Bologna and Cavallo, 2002) and thus, the same has been adopted to model stock return
volatility. ARCH and GARCH models have become widespread tools for dealing with time
series heteroskedastic models. The goal of such models is to provide a volatility measure--like a
standard deviation--that can be used in financial decision concerning risk analysis, portfolio
selection and derivative pricing.
5.2 - Description of Variables used in the Analysis
The variables used are as follows: NIFDR, NIFDRinf0, NIFDRinf1, NIFDRstf0,
NIFDRstf1, NIFDRopt0, NIFDRopt1, NIFDRder, INDFN, STFN, NIFJDR, S&P500DR,
INDFTO and INOPTN.
NIFDR (NSE Market Return):- This is an index of daily NSE stock market return
calculated from the NSE Nifty CNX 50, the share price index having fifty blue chip
shares companies.
NIFDRinf0:- NSE return for the period of pre index futures introduction
calculated
from the daily closing price of Nifty 50.
NIFDRinf1:- NSE return for the period of post index futures introduction calculated
from the daily closing price of Nifty 50.
NIFDRstf0:- NSE return for the period of pre stock futures introduction calculated from
the daily closing price of Nifty 50.
NIFDRstf1:- NSE return for the period of post stock futures introduction calculated
from the daily closing price of Nifty 50.
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NIFDRopt0:- NSE return for the period of pre index options introduction calculated
from the daily closing price of Nifty 50.
NIFDRopt1:- NSE return for the period of post index options introduction
calculated from the daily closing price of Nifty 50.
NIFDRder: - NSE return for the period of 2002-2006 to analyse the impact of
derivatives turnover calculated from the daily closing price of Nifty 50.
NIFJDR:- (NSE Market Return):- This is an index of daily NSE stock market return
calculated from the NSE Nifty Junior 50, the share price index having fifty blue chip
shares companies.
S&P500DR:- This is an index of daily USA stock market return calculated from the
S&P500 index, the share price index having 500 blue chip shares companies.
INDFN: - This is the indicator of a dummy variable for stock index futures in NSE Nifty
50 Index.
STFN: - This is the indicator of a dummy variable for stock futures in NSE Nifty 50
Index.
INOPTN: - This is a dummy variable for stock index options introduced in NSE Nifty
50 Index.
INDFTO: - This is turn over of the index futures for the period of 2002-2006. This
variable is proxy for derivatives turn over in the stock market.
All the stock market returns are calculated from the daily closing prices of indices
applying the log of the ratios of the related indices. The formula may be written as Raju
(2003);
22
Rt
=
ln(Ct / Ct-1)
Where,
Rt
=
Stock Market Return
ln
=
Natural Log,
Ct
=
Closing Price of index at time t
5.3 - Unit Root Test
As we have used return variables calculated from log values, we do not need to test the
problem of stationarity. But because of it being a compulsory condition for GARCH implication,
we have tested the stationarity for all the basic variables. To solve the problem of stationarity, the
Augmented Dickey-Fuller Test has been applied that is the most frequently used test for unit root
test.
Unit root, random walk and non-stationary are near about similar things. A formal test
model to solve the problem of stationarity was firstly proposed by Dickey and Fuller that is
known as Dickey - Fuller Test (DF Test). The model or procedure tests for the presence of a 'unit
root' in the time series. The DF test starts with the assumption that a series yt is following an
Auto Regressive (1) process of this form:
yt = a1 yt-1 + et
And then testing for the case that if the coefficient a1 is equal to one (unity), hence “unit root” or
Yt series is non stationary.
In case of a1 =1 then the above equation can be expressed as:
yt = et
23
And the yt series is said to be integrated of order one (I(1)) or non-stationary; while the
yt is integrated of order zero (I(0)) or stationary.
In fact instead of testing for a1 =1 we can test an alternative version of the same thing
using this equation:
yt =  yt-1 + et
And now testing whether =0, which is clearly equivalent to the above mentioned case.
Dickey and Fuller (1979) actually consider three different regression equations that can
be used to test for the presence of a unit root:
yt =  yt-1 + et
yt =a +  yt-1 + et
yt = a +  yt-1 + a2 t + et
The difference between the three regressions concerns the presence of the deterministic
elements a and a2.
The parameter of interest in all the regression equations is ; if =0, the series contains a
unit root. The test involves estimating one (or more) of the equations above using OLS in order
to obtain the estimated value of  and associated standard error. Comparing the resulting tstatistic with the appropriate value reported in the Dickey-Fuller tables allows the researcher to
determine whether to accept or reject the null hypothesis =0.
The most frequently used test for unit roots is the augmented Dickey-Fuller test, an
advanced form of DF Test. The ADF test simple includes AR(p) terms of the yt term in the
three alternative models. Therefore we have:
24
n
yt =  yt-1 +
  y
i
i 1
n
yt =a +  yt-1 +

i 1
i
t  i + et
y t i + et
n
yt = a +  yt-1 + a2 t +
  y
i 1
i
t i
+ et
The difference between the three regressions again concerns the presence of the deterministic
elements a and a2. The lag length n should be determined according the AIC and SBC criteria.
Also, note that in the ADF tests note that we use different statistical tables with critical values in
each case.
The t-test for  2 is called the (TAU)  t - statistic for which Dickey and Fuller have
computed the relevant critical values.
6 - Interpretation of Results
In this section the result tables and figures are given with its result interpretation. First,
simple statistics have been tested then GARCH models are estimated.
[Insert table 2 here]
In the table-2, we have analyzed the volatility (S. D) of NSE Nifty 50 for pre and post
period of introduction of derivatives with some other statistical results, and found that the
volatility in the NSE (calculated from NIFDR and) has a decreasing trend after introduction of
the derivatives as the S D values have gone down. This trend can be seen also by the graph-1 and
2 given in appendix.
[insert graphs here]
25
6.1 - Result of Unit root test
The initial stage of analysing a prepared time series data is for GARCH estimation is test
the problem of unit root. If the time series data is not stationary, the regression result will be
spurious. The level of significance and r2 value may be high but of no use and the result will not
be significant. So at first the stationarity of the time series is tested employing Augmented D F
test.
Null hypothesis H0: z(t) is a unit root process: a = 0.
Alternative hypothesis (H1): z(t) is stationary process: a < 0.
The test statistic is the t-value of ‘a’.
[insert table 4]
Table-4 shows the result of ADF test. It is clear from the table that all the return
variables that are calculated from the log value are stationary as there p-values are 0.00. So H0 is
rejected in favor of H1 at the 1% significance level. The derivatives turnover variable (INDFTO)
is stationary for their first difference.
6.2 - Result of GARCH (1, 1) Estimate for NSE return
Models of GARCH error have been estimated for several set of variables. The return
series (NIFDR) is selected to test the models. NSE return is a dependent variable. The whole data
set is divided into two period of time, Pre-derivatives introduction period and post-derivatives
introduction period. First, the GARCH model has been tested with the dummy variables for
whole length of data for each set, and then the GARCH error has been examined for the pre and
post introduction period. After this it has been tested the derivatives impact adjusted with the
26
Nifty Junior (an index of NSE stock market). At last the impact or derivatives volume on the
stock market volatility is tested with the help of GARCH model.
Model - 1:
NIFDRt = CONS + a1NIFDRt-1 + a2INDFN + Ut
GARCH specification:
Ht = r1U2t-1 + r2H t-1 + b1INDFN + d
Where,
'U(t)' is the error of the OLS conditional expectation model,
'H(t)' is its conditional variance or sigma square (  2 ),
'd' is a constant of the GARCH model.
The two-sided p-values are based on the normal approximation.
Note: 1- the software package used for analysis estimates the ARCH and GARCH errors in the
same process. When ARCH effect was estimated, it gave the same result as it was found in the
GARCH specifications for coefficient of U2t-1.
2- There are several models to be tested and the analysis was being long, so it has been
considered that ARCH effect is present on the basis of GARCH Application.
Model -1 examines the impact of introduction of index futures on NSE stock market
return for the whole period under consideration. The result is tabulated in the table 5.
Note - The autocorrelation is tested by Ljung-Box Q statistics test. The LB (Q=7) test accept the
null hypothesis at the 5% significant level. The Breusch-Pagan test is used to see the
errors of homoskedastic with the null hypothesis that the errors are homoskedastic. The
test rejected the null hypothesis.
27
These tests are done for only this model. The other models having NSEDR
series are considered to be correct models.
[insert table-5]
The table-5 shows that the dummy variable for stock index futures (INDFN) is
significant. The coefficient of INDF (b1 = 0.001161) is significant at one per cent significant
level, which is indication of the fact that the introduction of index futures might have made a
difference in the volatility of NSE stock returns (NIFDR). But the expected negative sign is
absent for the coefficient of the dummy variable (INDFN). So it is concluded that index futures
have increased the volatility in the stock market. The coefficient of the GARCH ‘r1’ and ‘r2’ are
significant indicating that there persists the informational effect in the stock market volatility.
Both the recent and old news are present in the market.
Model - 2
NIFDRt = CONS + a1NIFDRt-1 + a2STFN + Ut
GARCH specification:
Ht = r1U2t-1 + r2H t-1 + b1STFN + d
[insert table-6]
Table-6 is related with the result of the impact of stock futures on the NSE return
volatility. It becomes clear from table-6 that the trading in stock futures are not significant
determinant of the volatility of the NSE stock market return as the coefficient (b1) of the dummy
variable STFN is not significant. But the negative sign indicates that the impact, whatever it may
be, is reducing the stock market volatility. In this equation model also the r1 and r2 are significant
indicating the presence of news effect on the return volatility.
Both the above tables are examining the impact of futures trading and the result supports
different hypothesis that the introduction of index future trading has not reduced the volatility but
28
the stock futures has reduced but insignificant in the NSE spot market return. For both the
futures products the GARCH coefficient (r 1 and r2) are significant indicating the presence of
informational impact on the stock market volatility. Further analysis in extended to test whether
the introduction of the futures has reduced the volatility in the period of post introduction or not.
This analysis is done in the next two models.
Model - 3:
NIFDRinf0t = CONS + a1NIFDRinf0t-1 + Ut
GARCH specification:
Ht = r1U2t-1 + r2H t-1 + d
[insert table-7]
Model - 4:
NIFDRinf1t = CONS + a1NIFDRinf1t-1 + Ut
GARCH specification:
Ht = r1U2t-1 + r2 H t-1 + d
[insert table-8]
Table 7 shows the result of GARCH estimate for pre-index futures introduction period
and Table 8 shows the result of GARCH estimate for post index futures introduction period. For
both the period GARCH effect is significant as it is clear from the p-value. The coefficients
reported in Table 7 and 8 show that in the GARCH variance equation, (r2) ‘old news’
components have gone up and r1 ‘recent news’ components have also gone up in the post Indexfuture period and these estimates are significant at one per cent level. It can be concluded that
introduction of the Index futures has increased the impact of recent news and reduced the
asymmetric information but at the same time, it extends the effect of uncertainty originating from
the old news.
29
The ‘r1’ component is the coefficient of square of the error term (ARCH effect) and the
‘r2’ represents the coefficient of the lagged variance term (GARCH effect) in the variance
equation. ARCH effect (the coefficient r1) is an indication of ‘recent news’ and GARCH effect
capturing the effect of ‘old news’ (Antoniou and Holmes’ (1995), Bologna and Cavallo’s (2002),
Shenbagaraman (2003)). This estimation technique (GARCH) enables us to explore the link
between information/news arrival in the market and its effect on cash market volatility. The
advantage of a GARCH model is that it captures the tendency in financial data for volatility
clustering.
The period of the introduction of the stock futures is different and result of model 2 has
shown that stock future trading is reducing the volatility, though not significantly. It is useful to
test its impact in the pre and post introduction period. The models 5 and 6 contain the analysis.
Model - 5:
NIFDRstf0t = CONS + a1NIFDRstf0t-1 + Ut
GARCH specification:
Ht = r1U2t-1 + r2H t-1 + d
[insert table-9]
Model - 6:
NIFDRstf1t = CONS + a1NIFDRstf1t-1 + Ut
GARCH specification:
Ht = r1U2t-1 + r2H t-1 + d
[insert table-10]
The tables 9 and 10 have the result of the impact of pre and post introduction of stock
future. The result is not supporting the result that stock futures has reduced volatility in the stock
market as it suggests that the introduction of the stock futures in NSE has enhanced the volatility
30
in the stock market by increasing the uncertainty (as the old news effect has increased in the post
introduction of stock future period) in the Market. This problem may be because of stock futures
are significant factors affecting the volatility.
Now it would be preferable if the impact of the other important derivatives products, that
is called options, is also examined as the results from the futures contracts are not so clear. The
next exercise is concerned with the options. The next three models are developed for this
purpose.
Model -7:
NIFDRt = CONS + a1NIFDRt-1 + a2OPTN + Ut
GARCH specification:
Ht = r1U2t-1 + r2H t-1 + b1OPTN + d
[insert table-11]
Table-11 shows the result of impact of index options on NSE volatility. The coefficient of
the dummy variable of index options (OPTN) is significant at 1% significance level suggesting
that the introduction of index options in NSE has impacted significantly the stock market
volatility and the negative sign indicates that options have reduced the volatility (risk) in the
stock market.
Finding favourable result now we will see what happen before and after introduction of
index options.
Model - 8:
NIFDRopt0t = CONS + a1NIFDRopt0t-1 + Ut
GARCH specification:
Ht = r1U2t-1 + r2H t-1 + d
[insert table 12]
31
Model - 9
NIFDRopt1t = CONS + a1NIFDRopt1t--1 + Ut
GARCH specification:
Ht = r1U2t-1 + r2H t-1 + d
[insert table 13]
It becomes clear from the tables 12 and 13 that for both the period the information impact
is significant and supporting the result of the table-11. After the introduction of index options the
coefficient of recent new (r1) has gone up and old news (r2) has gone down. This indicates the
uncertainties in the stock market have gone down and the volatility has been reduced. This result
rejects the null hypothesis that derivatives have not reduced the volatility of NSE spot market.
The above tests have resulted different things. As we have mentioned that we have taken
three time periods that are decided by three important derivatives products. Index futures were
introduced from June 2000 and 2000-2001 was the period of a big scam in the stock market.
Since 2002 the stock market was able to be taken its stable position and further even at present
the stock market has recorded an efficient position. This may be the reason that result for period
of options introduction is more trustable.
But the question is whether the derivatives products are the only reasons to
reduce/increase the volatility, or are there some others factors affecting the volatility of stock
market return? To solve this problem the other variables as NIFJDRt, S&P500DRt and
Derivatives turnover are included as explanatory variables to control the effect of the index
futures. The following models are related to this practice.
Model 10NIFDRt = CONS + a1 NIFDRt-1+ a2 INDFN + a3 NIFJDRt + a4S&P500DRt+ Ut
GARCH specification:
32
Ht = r1 U2t-1 + r2 H t-1+ b1 INDFN + b2 NIFJDRt + b3S&P500DRt + d
This model is constructed with the other variables which may be determinant of the Nifty
50 volatility besides derivatives products. The variables will control the impact of derivatives.
The result is tabulated in table-14.
[insert table 14]
It is clear from the result tabulated in table-14 that the coefficient b2 for Nifty Junior
return volatility is significant at 1% significant level with negative sign indicating that the other
factors (market factors) have significantly reduced the volatility in the stock market. The
significance of the index futures effect is cleared out while including some others variables. But
the world factors are not significant.
Overall findings from the econometric analysis is somewhat mixed, though indicating
that the stock market volatility has been effected significantly by derivatives trading. The stock
market volatility has followed a declining trend after the introduction of derivatives products
(stock index and index options) but not for the introduction of Index futures. The informational
efficiency has been increased after the introduction of derivatives trading. It has been argued that
the introduction of derivatives would cause some of the informed and speculative trading to shift
from the underlying cash market to derivative market given that these investors view derivatives
as superior investment instruments. This superiority stems from their inherent leverage and lower
transaction costs. The migration of informed traders would reduce the information asymmetry
problem faced by market makers resulting in an improvement in liquidity in the underlying cash
market.
It is interesting to explore further whether the nature of the GARCH process was altered
as a result of the derivatives introduction. We therefore estimated the GARCH model separately
33
for the pre-futures and the post-futures period separately. The first point to note in comparing the
results before and after futures introduction is that the onset of futures trading has altered the
nature of the volatility. Before futures, the ARCH and the GARCH effects are significant,
suggesting that both recent news and old news had a lingering impact on spot volatility.
The migration of informed traders would reduce the information asymmetry
problem faced by market makers resulting in an improvement in liquidity in the underlying cash
market. In addition, it could also be argued that the migration of speculators would cause a
decrease in the volatility of the underlying cash market by reducing the amount of noise trading.
This hypothesis is correctly certified by the study that derivatives trading (for the introduction of
index option 2001-2006) have reduced the stock market volatility.
For the period of introduction of stock futures, it has been found that the result for this
products time period is not very clear but in general, has increased the volatility in the Indian
stock market. This was the period when stock market was facing too much fluctuation period.
The result supports some empirical finding that derivatives market is a market for speculators.
Traders with very little or no cash or shares can participate in the derivatives market,
which is characterised by high risk. Thus, it is argued that the participation of speculative traders
in systems, which allow high degrees of leverage, lowers the quality of information in the
market. These uninformed traders could play a destabilising role in cash markets (Chatrath,
Ramchander and Song, 1995). However, according to another viewpoint, speculation could also
be viewed as a process, which evens out price fluctuations.
The debate about speculators and the impact of futures on spot price volatility suggests
that increased volatility is undesirable. This is, however, misleading as it fails to recognize the
link between the information and the volatility. Prices depend on the information currently
34
available in the market. Futures trading can alter the available information for two reasons: first,
futures trading attract additional traders in the market; second, as transaction costs in the futures
market are lower than those in the spot market, new information may be transmitted to the
futures market more quickly. Thus, future markets provide an additional route by which
information can be transmitted to the spot markets and therefore, increased spot market volatility
may simply be a consequence of the more frequent arrival and more rapid processing of
information. (Bandivadekar and Ghosh 2005)
7 - Conclusion
This study has examined the informational effects of the derivatives trading on the
volatility of stock market with the help of a well known test for the volatility of the financial time
series ARCH/GARCH model. NSE Nifty 50 is used as the proxy for stock market return. The
general finding is that introduction of derivatives trading has significant impact on the volatility
of the stock market return. For the assurance of the result three derivatives products have been
used for different time periods.
To control the impact of the derivatives trading, we used some other return series and
found that derivatives are not a single factor affecting the stock market risk (volatility). There are
some other market factors also. A lot of efforts have been done by SEBI to control the volatility
of the NSE market.
High volatility is considered as high risk in the stock market. To reduce this risk factor in
the Indian stock market, a number of steps are being adopted by the market regulators.
Introduction of derivatives trading is one of them. The analysis concluded that the derivatives
trading have done its work. It has enhanced the efficiency of the stock market by reducing the
spot market volatility.
35
The result is different for the different periods. As, for the period of June 2000- June
2006, the analysis concludes that the volatility is increasing due to derivatives trading and for the
period of July 2001-June 2006, spot market volatility is following decreasing trend due to
Derivatives trading. This variation may be because of an artificial fluctuation in the stock market
due to big scam 2001 as it happened in the mid of 2001. This was also the reason why we used
three time periods. Anyway, we have considered more real result that is concluded for the period
of index options trading.
But the present increasing nature of the volatility is a subject of caution. Though the
trading through derivatives in increasing day by day and more new derivatives products have
been introduced, the volatility is not much controlled. The functioning area or the size of the
market has been speeded enough. In this situation strong regulatory system is desired for wellfunctioning of the stock market.
36
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www.bseindia.com
38
Tables and Figures
Table 2:- Descriptive Statistics for NSE Return (Jan 1998-June 2006)
Time periods
Mean
S. D.
Max.
Pre INDF
0.000468
0.019386
Post INDF
0.000486
0.014652
0.07539
0.079691
Pre STF
-5.885E-05
0.0183268
-0.057202
Post STF
0.0009329
0.0140794
0.0796909
Pre OPT
2.622948E-05
0.0186558
0.075393
Post OPT
0.00079976
0.0141453
0.07969091
Graph 1:- Trend of Volatility in Nifty 50 for the Period of Jan 1998-June 2006
NIFDR Daily Volatility
0.16
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0.12
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2110
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Time Period
NIFDRDV
Graph 2:- Trend of Volatility in Nifty Junior for the Period of Jan 1998-June 2006
39
NIFJR Daily Volatility
0.16
0.14
0.12
Volatility
0.1
0.08
0.06
0.04
0.02
0
10
1
11
2
12
3
13
4
14
5
15
6
16
7
17
8
18
9
19
20
21
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23
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25
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30
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42
43
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45
46
47
48
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50
51
52
53
54
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56
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58
59
60
61
62
63
64
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66
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68
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70
71
72
73
74
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82
83
84
85
86
87
88
89
90
100
91
101
92
102
93
103
94
104
95
105
96
106
97
107
98
108
99
109
110
111
112
113
114
115
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679
680
681
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719
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731
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981
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1000
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1001
992
1002
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1003
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1006
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1007
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1008
999
1009
1010
1011
1012
1013
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1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
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1029
1030
1031
1032
1033
1034
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1036
1037
1038
1039
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1080
1081
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1102
1103
1104
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1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
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1133
1134
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1177
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1190
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1199
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1234
1235
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1371
1372
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1471
1472
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1911
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1989
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1991
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1998
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2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
Time Period
NIFJRV
Table 4:- Result of Unit Root Test
Variables
Para. estimate
t-value
p-value
S&P500DR
-1.2241
-8.3983
0.00000
NIFDR
-1.0072
-8.4091
0.00000
NIFJR
-0.7603
-7.8033
0.00000
Table - 5: Result of GARCH (1, 1) Estimate for NSE Return for whole time Period with
Index Futures
Parameters
Par. Estimate
r1
0.211263
r2
0.751943
b1
0.001161
d
0.000022
L B Q(7)
5.89
Breusch-Pagan test
97.044513
R-square
Number of Observations
Akaike Information criteria
t-value
12.268
46.828
1.811
5.996
[p-value]
[0.00000]
[0.00000]
[0.05016]
[0.00000]
0.81732
0.00000
= 0.1801
= 2130
-8.075541
Table - 6: Result of GARCH (1, 1) Estimate for NSE Return for whole time Period with
Stock Futures
Parameters
Par. estimate
r1
0.311714
r2
0.558765
b1
-0.000690
d
0.000060
R-square
Number of Observations
t-value
10.035
17.047
-1.163
6.826
[p-value]
[0.00000]
[0.00000]
[0.24484]
[0.00000]
0.1803
2130
40
Akaike Information Criteria
-8.062343
Table - 7: Result of GARCH (1, 1) Estimate for NSE Return Pre-introduction of Index
Futures
Parameters
a1
r1
r2
d
Par. estimate
-0.390403
0.181832
0.014549
0.000427
t-value
-11.828
3.587
0.208
8.585
= 0.2199
= 615
-7.499612
R-square
N. O.
Akaike Information criteria:
[p-value]
[0.00000]
[0.00034]
[0.83555]
[0.00000]
Table - 8: Result of GARCH (1, 1) Estimate for NSE Return Post-introduction of Index
Futures
Parameters
a1
r1
r2
d
Par. estimate
-0.344265
0.265994
0.688073
0.000026
t-value
-12.470
10.690
29.300
5.496
= 0.1478
= 1513
-8.292467
R-square
Number of observations
Akaike Information Criteria
[p-value]
[0.00000]
[0.00000]
[0.00000]
[0.00000]
Table - 9: Result of GARCH (1, 1) Estimate for NSE Return Pre-introduction of Stock
Futures
Parameters
Par. estimate
a1
-0.410058
r1
0.375793
r2
0.545186
d
0.000082
R-square
N. O.
Akaike Information Criteria
t-value
-11.956
6.249
9.445
4.034
= 0.1987
= 970
-7.698924
[p-value]
[0.00000]
[0.00000]
[0.00000]
[0.00005]
Table 10: Result of GARCH (1, 1) Estimate for NSE Return Post-introduction of Stock
Futures
Parameters
Par. estimate
a1
-0.384204
r1
0.306282
r2
0.619023
d
0.000033
R-square
NO
Akaike Information Criteria
t-value
-11.567
14.488
49.334
6.481
0.1558
1158
-8.369675
[p-value]
[0.00000]
[0.00000]
[0.00000]
[0.00000]
Table - 11: Result of GARCH (1, 1) Estimate for NSE Return for whole time Period with
Index Options
Parameters
r1
r2
Par. estimate
0.220373
0.719303
t-value
12.874
42.228
41
[p-value]
[0.00000]
[0.00000]
b1
d
-0.002180
0.000025
-3.817
6.416
0.1722
2130
-8.071036
R-square
Number of Observations
Akaike Information Criteria:
[0.00013]
[0.00000]
Table - 12: Result of GARCH (1, 1) Estimate for NSE Return Pre-introduction of Index
Options:
Parameters
Par. estimate
a1
-0.391975
r1
0.363038
r2
0.496792
d
0.000118
R-square
NO
Akaike Information Criteria:
t-value
-10.917
5.083
8.228
11.380
= 0.2033
= 877
-7.634702
[p-value]
[0.00000]
[0.00000]
[0.00000]
[0.00000]
Table - 13: Result of GARCH (1, 1) Estimate for NSE Return Post-introduction of Index
Options
Parameters
Par. estimate
a1
0.001567
r1
0.452367
r2
0.328460
d
0.000110
R-square
N. O.
Akaike Information Criteria:
t-value
3.591
7.388
6.746
40.112
0.0293
1251
-8.496515
[p-value]
[0.00033]
[0.00000]
[0.00000]
[0.00000]
Table-14: Result of GARCH (1, 1) Estimate for NSE Return for the whole Period Adjusted
by Nifty Junior and S&P500 Return
Parameters
Par. estimate
r1
0.285322
r2
0.637717
b1
0.000214
b2
-0.136321
b3
0.010703
d
0.000040
R-square
NO
Akaike Information Criteria:
t-value
10.329
23.346
0.342
-10.912
0.537
5.926
0.1866
2096
-8.113204
42
[p-value]
[0.00000
[0.00000]
[0.73267]
[0.00000]
[0.59148]
[0.00000]