Transcript of "Impact of Derivative Trading on the volatility of the underlying asset"
IMPACT OF DERIVATIVE TRADING ON THE VOLATILITY
OF THE UNDERLYING ASSET – ITC Ltd
Financial Time Series
Prof. Devi Prasad Bedari
IMPACT OF DERIVATIVE TRADING ON THE VOLATILITY OF THE UNDERLYING
STOCK – ITC LIMITED
Despite the reforms of nineties the level of concentration in trading as well as speculative trading is very
high in the case of secondary stock market. Hence, derivative trading was introduced to attract much of
the speculative transactions and to enable investor to choose the level of portfolio risk. The efficiencies
of these markets complement each other.
In derivative trading, there are a set of information seekers who help improve market efficiency –
hedgers, arbitrageurs and manipulators. While hedgers and arbitrageurs facilitate the linking of spot
market prices with the derivative market price, the manipulators role in manipulation of the market by
taking huge leverage cannot be ignored. Based on the purpose for which the derivative instrument is
used the volatility of the stock would be reduced or increased during the post‐derivative period.
The aim of the study is to analyze the impact of additional information generated due to introduction of
individual stock derivative instrument on the volatility of returns on the underlying stock – ITC Ltd. The
study first tests for asymmetric response in the period before introduction of derivative instruments,
after introduction of derivative instrument and for the full period. Later by using the appropriate model,
it deduces the impact of derivative trading in the volatility of the stock – ITC Ltd.
Since, the underlying asset being analysed is a stock or an index, the probability of the series being
characterized by heteroskedasticity is very high. Hence, the present study begins by examining the
presence of heteroskedasticity in the asset return series. The results indicated presence of
heteroskedasticity. Following this the stock returns are also tested for stationarity. Consequently, it is
hypothesized that the asset returns series follows a GARCH process.
The GARCH Model is as described below:
Mean Equation: Rt = c + ut, where ut~N(0,ht)
2 2 2
Variance Equation: 0 1 1 1 1
where, Rt is the log returns of the underlying asset, ut is assumed to be independently and identically
distributed with mean zero, ht represents conditional variance in period t, α1 describes the ‘news
coefficient’ (impact of one time period old news) and β represents the ‘persistence coefficient’ (impact
of news older than one time period).
However, the standard GARCH models assume symmetry in the response of volatility to information. If
the response is asymmetric, then the standard GARCH models will end up mis‐specifying the
relationship and further inferences based on this model may be misleading. However, GJR Model and
EGARCH model can be used to model the asymmetry.
GJR Model: ,
where It-1 = 1, if ut-1 < 0
= 0 otherwise.
EGARCH Model: ln ln
| | 2
In the present study, firstly, the existence of asymmetric response is tested individually for each asset,
for all three time periods, i.e.: (i) pre introduction of derivatives, (ii) post introduction and (iii) full period.
Then from the appropriate model, so generated GARCH coefficients would be used to analyze the
1) Conditional variance: Assuming that the conditional mean (of ht ) is constant and equal to zero, and
that α1+β <1, the unconditional variance of the standard GARCH model can be expressed as:
2) To study the relationship between information and volatility following the onset of derivatives
trading, a dummy variable is introduced in the conditional variance equation with the dummy
variable D taking on the value zero pre, and one post introduction of derivatives.
EGARCH: ln ln
| | 2
If , the coefficient of the dummy variable, is statistically significant, then it can be said that existence
of derivative trading has had an impact on spot market volatility. Further, the sign of indicates the
direction of change in the spot market volatility. If the coefficient is negative, it can be said that the
volatility has reduced post introduction of derivatives and vice versa if the coefficient is positive.
However, the reduction in volatility may be simply because of the impact of market pervasive factors.
Hence, it is necessary to separate the volatility arising from market wide factors. Hence the following
mean equation is used while studying the impact of derivatives on the volatility of the underlying stock.
Rt = c + δRNifty + ut
The impact of derivative trading is studied only in the case of the stock ITC Ltd. The derivative trading for
this stock has commenced by May 2005. The study analyses daily closing prices of each stock for the
period January 1997 to March 2009. In order to map the effect of market pervasive factors that affect
the volatility of stock returns, returns on nifty was used for that same time frame. The data on closing
prices for stock ITC Ltd and Nifty Index was obtained from NSE website. The log return of the asset is
calculated as Rt = ln .
RESULTS AND ANALYSIS:
The return of the stock ITC Ltd and Nifty were tested for stationarity using Augmented Dickey Fuller
Test. It was found that the level series of the returns were stationary and hence t‐statistic can be used to
interpret the significance of the variable. The results of the test are as follows:
ADF Test RITC RNIFTY
t‐statistic ‐55.5137 ‐51.9558
p‐value 0.0001 0.0001
The summary statistic of the three time periods analysed was calculated. The Jarque‐Bera (JB) test is
based on the result that a normally distributed random variable should have a skewness equal to zero
and kurtosis equal to three. The results of Lagrange Multiplier (LM) test examining the presence of
autocorrelation in squared residuals is also given below. The test is conducted up to a lag of 12 and both
the JB test statistic and LM test statistic follows a chi‐square distribution.
ITC Mean Std Dev Skewness Kurtosis JB LM
Overall Period 0.066988 2.392207 ‐0.00947 5.505908 799.383 317.537
Pre‐Derivative 0.06853 2.477688 ‐0.0147 5.77811 670.5673 209.7054
Post‐Derivative 0.065823 2.198581 0.003506 4.288161 66.99863 90.18397
It was found that the skewness is non‐zero and the kurtosis is in excess of three. Further, the JB test
indicates that the assumption of normality is violated by log return series. Finally, the LM statistic
suggests that in almost all the cases the squared residuals are autocorrelated, thus confirming the
presence of ARCH effects in the time series analyzed. From the graph of return on the stock ITC Ltd, It
can be found that there is a tendency of large changes in stock price (of either sign) to follow large
changes and small changes (of either sign) to follow the small changes. In other words, current level of
volatility tends to be positively correlated with its level during the immediately preceding levels. This
tendency is called volatility clustering. ARCH Model can be used effectively to model volatility clustering.
Return of ITC ‐ Volatility Clustering
1 1501 3001
Consequently, in order to study the impact of information on volatility of stock returns, a Generalized
ARCH measure of volatility would be enough. However as most of the financial series possess
asymmetric response; test for asymmetric response is performed using GJR and EGARCH Model. The
result of the GJR Model is as below:
LM Test Unconditional
GJR Model α0 α1 β
Obs. R p‐Value variance
Overall Period 0.2074*** 0.0689*** 0.8713*** 0.0473*** 9.2672 0.5069 5.7681
Pre‐Derivative 0.1447*** 0.0640*** 0.8977*** 0.0308** 10.22121 0.5965 6.3598
Post‐Derivative 0.4004*** 0.0549*** 0.8029*** 0.1129*** 5.604562 0.8473 4.6793
Note: Numbers denote significance level at *** (1%), ** (5%) and * (10%) level respectively.
The value of was highly significant confirming the asymmetric leverage effect i.e., asymmetry in
responding to the good and the bad shocks. It is found that increase in volatility was high with the
occurrence of negative shock rather than that while effected during the positive shock. Post‐
introduction of derivative, the asymmetric effect also seems to have increased and this is evident from
the high values of for the post‐introduction period. There is no autocorrelation of the residuals
resulting from the GJR Model and this is evident from the chi‐square test. The observed R values and the
respective probability results of the LM Autocorrelation test is also provided in the table. The Null
hypothesis “there is no auto correlation is not rejected”. The long run (unconditional) variance in the
case of GJR model given by Andersen et. al. (2005) is as below:
It is clear from the GJR Model that the unconditional volatility has decreased after derivative trading was
allowed in the stock ITC Ltd.
The results of EGARCH Model are as given below:
EGARCH ω β α
Obs. R P Value
*** *** *** ***
Complete Period ‐0.0745 0.9627 ‐0.0426 0.1790 12.3476 0.2624
*** *** *** ***
Pre‐Derivative ‐0.0760 0.9778 ‐0.0382 0.1517 14.7121 0.1429
*** *** ***
Post‐Derivative ‐0.01997 0.8932 ‐0.0854 0.2289 5.9364 0.8205
*** ** *
Note: Numbers denote significance level at (1%), (5%) and (10%) level respectively.
The significance of the sign effect variable is also high and found to be negative. This confirms the
asymmetric effect in the underlying stock ITC Ltd. Post‐introduction of the Derivatives, it is also
observed that the ITC stock had higher sign and size effect which is evident from the values of and α
which is very high compared to the period before the introduction of derivative. It is found that increase
in volatility was high with the occurrence of negative shock rather than that while effected during the
positive shock. The residual test – LM Autocorrelation test also confirmed the absence of
autocorrelation in residuals.
In order to analyze the overall impact of introduction of derivatives on the conditional volatility of the
spot market, a dummy was incorporated while specifying the volatility dynamics. The dummy would
take a value zero in the pre‐introduction period and one post. The results of the GJR Model indicate that
the coefficient of the dummy variable is negative but significant only at 18 %. But from EGARCH Model it
could be observed that that the coefficient of the dummy variable is negative and significant at 2% .
GJR Model c δ α0 α1 β 1 2 LM Test
ITC Ltd 0.0425 0.7840 0.1946 0.0871 0.8632 ‐0.0031 ‐0.0182 7.3841
Signif. (p‐value) 0.1933 0 0 0 0 0.8132 0.1773 0.6887
EGARCH c δ Omega β 1 α 2 LM Test
ITC Ltd 0.0443 0.7789 ‐0.0774 0.9521 0.0039 0.1846 ‐0.01173 7.6577
Signif. (p‐value) 0.167 0 0 0 0.6355 0 0.0141 0.6622
Thus, it can be said that introduction of derivatives trading has resulted in reduction in spot market
volatility. The asymmetric effect in the above model has become insignificant in both GJR and EGARCH
Model. One probable reason could be much of the asymmetric behavior of the stock price of ITC would
have been explained by the asymmetric behavior of the stock index NIFTY which is being included in the
Mean equation for the study of impact of derivative. The asymmetric effect of NIFTY can be observed
below from its estimates of GJR and GARCH Model.
GJR Model α0 α1 β
Obs. R p‐Value
NIFTY 0.1344*** 0.0547*** 0.8210*** 0.1546*** 5.076
EGARCH ω β α
Obs. R P Value
*** *** *** ***
NIFTY ‐0.1301 0.9381 ‐0.1098 0.2414 5.9155 0.8223
Note: Numbers denote significance level at *** (1%), ** (5%) and * (10%) level respectively
It was found that the volatility of the stock ITC Ltd had both the leverage effect and volatility clustering.
The derivative trading is introduced to influence price discovery, faster information movement, and to
minimize the risks through opportunities like hedging. But derivative can also used to manipulate the
market and thus could also result in increase in volatility. From the analysis, it was observed that the
post introduction of derivatives the stock ITC Ltd had higher asymmetric effect. It was also observed that
the volatility has reduced significantly after the introduction of derivatives. Hence it is concluded that
the derivatives market had been instrumental in pulling the stock price down as a response to the
negative shock and also has reduced the volatility of the returns of the stock.