Volatility informed trading in the options market: evidence from India.
Pathak, Rajesh
Introduction
While financial theory has well emphasized the role of derivatives
in trading a gamut of risks in financial markets (such as equity risk,
exchange rate risk, interest rate risk, and credit risk), their role as
a vehicle to trade on information has emerged as an additional economic
function in empirical financial research. Market microstructure theory
suggests that, price movements are largely caused by the arrival of new
information and their incorporation into market prices through trading.
A sizeable literature (1) have documented the use of derivatives on
directional information and their role in predicting future price
movements but, the corresponding issue of trading of derivatives based
on non-directional information, like information about future
volatility, remains to be examined in literature in detail. Since
volatility forecast is central in finance due to its use in pricing of
derivatives as well as for financial activities like portfolio selection
and asset management, a study on volatility informed trading of
derivatives becomes essential.
The theory of options pricing is unclear about the exact nature of
volume-volatility relationship (Sarwar 2005). Black (1975) argues that
informed traders may be attracted towards options due to the economic
benefits like lower transaction cost and higher leverage associated with
trading options. As a result, the option trades may be informative about
future price volatility due to the fact that pricing options requires
volatility as an input parameter. Conversely, researchers also argue the
hedge related use of options arising due to asset's price
volatility, which may cause option trading to follow the price
volatility. This study examines the relationship between implied
volatility and the trading activity of options to understand the kind of
use options have in the Indian market and thus contributes to the
literature on the price discovery function of derivatives.
Options are securities with non-linear payoff structure. As a
result, a volatility informed trader can only bet on his information in
options market (unlike a trader with directional information who,
besides options, can also trade stocks or futures). Lack of empirical
proof of this fact stimulates us to conduct this study. Moreover, as the
focus of microstructure literature has been on intraday pattern rather
than inter-day dynamics, studies using publically available data with
daily frequency are very sparse. Besides, a large number of small
traders who are unable to incur the cost to access private information
trade mostly on freely available information. Thus, a study
investigating the volatility related information contained in options
trading using publically available daily data is imperative. It would
benefit the traders at large in maximizing their payoffs. The data of
S&P CNX Nifty index options traded on National Stock Exchange (NSE),
India is employed for this study. This study, to the best of our
knowledge, is the first to address the issue of volatility informed
trading of options in Indian market.
Our study period i.e. January 2004-December 2011, is considerably
longer period compared to that of the existing studies and includes
years of up, down, and recovery trends in the market. Derivatives are
popular instrument to trade on negative news due to short selling
restrictions in spot market. Moreover, options in different moneyness
categories offer different leverage and liquidity and they also have
different future volatility estimates (Shaikh, Padhi 2014). These
factors may have implications for participants in the market as it can
significantly affect their payoffs. Thus, we consider market trends and
option's moneyness classes in our analysis to uncover a particular
trend or moneyness class (if any) which is preferred by informed traders
or hedgers.
The next section presents a brief literature review. Section 3
highlights the objective of the study and section 4 discusses, in
detail, the data and methodology used for this study. Section 5 presents
the empirical results of the study and section 6 concludes it.
1. Literature review
Latane and Rendleman (1975) are the first to examine the
information content of implied volatility about option prices. As the
sensitivity of option contracts across series of options vary, they
employ weighted implied standard deviation (WISD) as a measure of market
forecast of return variability (computed by weighting the implied
volatility of series of options on a given day by sensitivity of option
price to implied volatility). They use options data of 24 companies
listed on Chicago Board of Options Exchange (CBOE) and address three
main objectives in the study. First, they study the usefulness of WISD
in identifying over or under priced options and thereby reducing risk in
hedge positions. Secondly they examine relationship between WISD and
ex-post volatility and further they test the stability of the cross
sectional average of WISD. They report the following results. The
portfolio based on WISD price projections produces significant abnormal
returns, which confirms the usefulness of WISD in determining proper
hedge positions and identifying over and under priced options. They
report significant correlation between WISD and ex-post volatility,
which proves WISD as a better estimate of future volatility. Regarding
the stability of cross sectional average of WISD they report strong
tendency of volatility to move together with time.
Chiras and Manaster (1978) compare the predictability of historical
volatility and weighted implied volatility for future stock returns
variance. They report that options implied volatility is a better
predictor of realized stock returns volatility. Beckers (1981) studies
the predictive accuracy of implied standard deviation (ISD) for future
price variability and finds that option implicit standard deviation is
an efficient measure of future price variability. However, Canina and
Figlewski (1993) study the S&P 100 Index options for the period
March 15, 1983 to March 28, 1987 and document that implied volatility
(IV) computed using Black-Scholes options pricing formula is
inefficient, biased and inferior estimate of market's future
volatility forecast, when compared to historical volatility.
Chen, Cuny and Haugen (1995) study the relationship between stock
volatility, basis (2) and open interests in futures market using S&P
500 Index. They base their study on the intuition that when volatility
increases in the market, investors prefer to entice more people in the
market for risk sharing. Those investors reduce their risk exposure not
only by selling their stock upholding alone but also by selling related
futures contract. Such activity may result in decreasing basis and
increasing open interest due to enhanced participation into the market.
They find that increase in expected volatility results in decrease in
basis and increase in open interest.
Kyriacou and Sarno (1999) have examined the dynamic relationship
between derivatives trading and volatility of the underlying asset using
daily data of FTSE 100 Index, its futures and options. The trading
activity is measured by daily futures and options volume standardized by
open interest whereas cash index volatility is estimated alternatively
by adjusted daily price changes, daily price changes, squared return and
GARCH(1,1). They follow Koch (1993) and use simultaneous equation model
to examine the relationship as opposed to vector-auto regression, which
does not allow for simultaneity and possibly can cause misspecification
problems. They report that expected future volatility, futures volume
and options volume are determined in a system of equations that allows
for both simultaneity and feedback.
Mayhew and Stivers (2003) study the information content of implied
volatility about firm level volatility using options on 50 most highly
traded stocks listed on CBOE during 1988-1995. They report that for most
actively traded options the implied volatility subsumes almost all
information about firm level volatility. However, results of this study
are biased towards actively traded stocks and cannot be generalized.
Sarwar (2005) studies the relationship between expected future
volatility of S&P 500 Index and aggregate options volume. He
conducts the study separately for call and put options and for moneyness
classes. He, for the most part, reports strong feedback relationship
between the options volume and expected future volatility, however
results for at-the-money (ATM) and out-of-the money (OTM) options are
found to be more pronounced.
Ni, Pan and Poteshman (2008) study whether options volume is
informative about future volatility of the underlying assets. Motivated
by the unique characteristics of options market that it suits to
volatility informed investors well, they conduct this study employing
unique dataset of stock options trade provided by CBOE over the period
of 1990 to 2001. They argue that if the option volume is informative
about future stock volatility then non market maker net demand for
volatility should be positively related with future stock volatility.
They compute the non market maker demand for volatility by aggregate sum
of net options volume (both call and put) weighted by options vega (3)
across strike prices. They test the relationship using multiple
regression framework where realized volatility (RV) is regressed against
non market maker demand for volatility along with a set of control
variables (lags of RV, lags of implied volatility, dummy for earning
announcement date, stock volume and options volume). They report
significant positive relationship between options non market maker
demand for volatility and subsequent realized volatility. They further
argue that some options market trades represent bets both on volatility
and direction (for example, a naked call buyer benefits both from
increasing stock price and increase in volatility) whereas other trades
like straddles (4) are primarily bets only on volatility. If the
predictability reported earlier is due to informed volatility trading
then the straddle type of trades should have stronger predictability.
They conduct tests for the above argument by extracting the total
options demand for straddle trade from total non market makers demand
for options and find that demand, which is due to straddle trade, are
strong predictor of volatility compared to demand that were not straddle
trade.
Based on the literature review, we make the following observations.
First, Implied volatility from options market is an efficient measure of
expected price volatility and second, that linkage of option trading
activity and exp ected volatility of underlying asset is not examined in
detail. We examine the same issue using implied volatility as a measure
of expected price volatility whereas daily number of contracts traded
and changes in open interest measure trading activity in options market.
2. Objectives
The objectives of the study are as follows:
--To examine the dynamic relationship between options aggregate
trading activity and expected future price volatility of the underlying
asset.
--To examine if the classes of options moneyness and the market
trends affect the direction and the strength of such relationship.
3. Data and methodology
We use options summary transaction data of S&P CNX Nifty index
provided by NSE, India. The summary transaction data includes expiry
date of the contracts, series of available exercise prices, type of
options (Call/Put), daily Open, High, Low, Close and Settlement prices
of Nifty index options, number of contracts traded, daily trading value
(Rs. in Lakh), daily open-interests (OI) and daily changes in OI. We
collect data for the period January 01, 2004 to December 31, 2011. We
follow Sarwar (2005) and exclude the options with trading volume of less
than 3 contracts and the expiry day transaction data. The Nifty index
options are European during the period of study. We observe that other
than long term index options (3 quarterly and 8 half yearly contracts),
which trade rarely, NSE has three month trading cycles and accordingly
three contracts namely near month, next month and far month contracts
are available for trade at any point in time. We find that near month
contracts are the most traded options and the volume starts shifting to
next month contracts around the expiry week of the near month contract.
For this study, we consider all the options where number of
contracts traded exceeds 3 irrespective of their maturities. On a given
day, trading activity is measured alternatively by aggregating the
number of contracts traded (hereafter referred as volume) and the
changes in open interests (COI) across strike prices and maturities. We
compute common implied volatility (CIV) as a measure of expected future
volatility by averaging the Black-Scholes implied volatility computed
for series of options on a day weighted by the sensitivity of option
price to implied volatility or options vega. We compute the common
implied volatility and measures of trading activity i.e. volume and COI
for call and put options separately.
To identify the market cycles we plot daily closing values of
S&P CNX Nifty index against period of study. Based on the graph
(Fig. 1) we segregate it into three periods namely Uptrend (January 01,
2004 to January 20, 2008), Downtrend (January 21, 2008 to May 17, 2009)
and Recovery phase (May 18, 2009 to December, 2011). The break dates are
selected after close observation of the index value and returns during
the period of study. Our examination indicates that on average market
went up during 2004-2007. The plot of index values shows that market
started moving down around January, 2008. A significant fall was
witnessed around third week of January, 2008 (January 15, 2008: 2 per
cent down, January 18: 3 per cent down) and on January 21, 2008 the
benchmark index fell by massive 8.7 per cent and this momentum continued
further too. This 8.7 per cent fall was among the 10 biggest falls of
the stock market thus far and one possible reason for this fall may be
the proposal of Securities and Exchange Board of India's (SEBI) to
tighten the rules for purchase of shares and bonds in Indian companies
through the participatory note (PN) route. Nonetheless, it is
interesting to note that in a way Indian market sensed the downturn
months before Lehman brothers announcement of bankruptcy i.e. on
September 15, 2008, which subsequently affected markets worldwide and
led to severe economic crisis.
Similarly, the index value plot also shows that the benchmark
Nifty50 index started recovering around mid of March, 2009 (for example
13th March: 3.8 per cent up, 23rd March, 4.7 per cent up and this
continued). However, glancing deeper, we find that on May 18, 2009 the
market went up by more than 16 per cent (hitting the third circuit level
for index i.e. 10 per cent, 12 per cent and then 15 per cent) and then
this trend continued. One of the reasons of this biggest surge was the
election results announced on May 16, 2009 (Saturday) that pronounced a
clear verdict on the government and that meant much awaited stability in
a country where we had many promising reforms blocked by warring
government allies. These events made us to identify January 21, 2008 and
May 18, 2009 as brake dates for new trends in the market. It is
noteworthy that in both Uptrend and Recovery, the market moves upward
but they are different phenomena. During Uptrend, the market touches new
highs for the very first time whereas, during Recovery the upward
movement gradually restores the earlier highs. We also classify options
in moneyness categories namely in-the-money (ITM), at-the-money (ATM)
and out-of-the-money (OTM) contracts following Chen et al. (2005) and
Chan et al. (2009).
[FIGURE 1 OMITTED]
ITM/OTM call options are options with strike price ranging from
80/105 to 95/120 percent of index value in spot market and corresponding
put options are options with strike price ranging from 105/80 to 120/95
percent of index value in spot market. Both ATM call and put options are
options with strike prices ranging between 95 to 105 percent of the
underlying index value i.e. S&P CNX Nifty Index. We consider a call
option deep-in-the-money (DITM) if strike prices are less than 80 per
cent and deep-out-of-the-money (DOTM) if strike prices are greater than
120 per cent, and vice-versa for a put option. However, due to very thin
trading (less than 1 percent) in DITM and DOTM options, they are not
considered for any further analysis in this study.
We use Granger causality testing approach to investigate the
relationship between future price volatility and options market trading
activity by estimating Tri-variate Vector-auto Regression (TVAR) model
where endogenous variables are common implied volatility, aggregate
volume and aggregate changes in open interests. Vector-auto Regression
model omits the contemporaneous interaction between variables however;
it is possible that these variables are concurrently determined. To test
this possibility we run following multiple regression (Eq. (1)) to
examine the contemporaneous relationship between the expected future
volatility and measures of trading activities.
Regression Model:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1) (5)
Here [h.sub.t] is CIV on day t, [Vol.sub.t] is aggregate options
volume and [COI.sub.t] is aggregate changes in open interests on day t.
[D.sub.u] and [D.sub.d] are dummies for Uptrend and Downtrend market
phases. [D.sub.u] takes the value 1 during Uptrend period and 0
otherwise whereas [D.sub.d] takes the value 1 during Downtrend period
and 0 otherwise. The Recovery Period is considered to be the reference
category here. Interaction terms are included due to objective of
examining any significant change in relationship between volatility,
volume and COI with change in market trends.
Following TVAR model is used to examine the causality where ht is
common implied volatility (CIV), [V.sub.t-i] are lags of aggregate daily
options volume, [O.sub.t-i] are lags of aggregate changes in daily open
interest (COI) and l is the number of lags in the regression. Before
running the TVAR the prerequisite of variables being stationary is
verified.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)
We expect [[alpha].sub.1i] and [[beta].sub.1i] coefficients to be
significant for options market to be informative about future volatility
whereas significant [[gamma].sub.2i] and [[gamma].sub.3i] coefficients
would mean the expected future volatility determining the trading of
options, meaning the use of options for hedging purposes. Here, lag
lengths l in each case is determined using Akaike Information criterion
(AIC).
Further, it is known that different options provide varying degree
of leverage and liquidity and the preference of options may also change
with change in market environment. Considering these issues, we examine
the possible change in relationship due to different market trends (Up,
Down and Recovery) and due to change in options moneyness (ITM, ATM and
OTM) by repeating the TVAR analysis using system of Equations (2) for
different market trends and classes of options moneyness after due
classification of the dataset.
4. Empirical results
Table 1 presents the summary statistics and the statistics of
stationarity and normality test on the key variables of call and put
options data across series of options aggregated for the period of
study. For call options, the proxy of expected future volatility
measured by common implied volatility (common_impvol) has an average of
23.71% with a standard deviation of 8.8% however the maximum and the
minimum values indicate that the expected daily volatility is not
stable. Unlike call options, the mean common implied volatility for put
options is found to be low i.e. 0.8% with a low standard deviation of
0.9%. The maximum and minimum volatility also suggest that expected
volatility of put options is relatively stable. The reported skewness
and kurtosis values suggest that sample data do not come from normally
distributed population (6).
We also conduct the unit root test to examine the stationarity of
all the three variables i.e. Common_implvol, Total_vol. and Total COI,
as a prerequisite for further use of these variables in time series
regressions. We conduct Augmented Dickey-Fuller Test (ADF test) for this
purpose and the hypothesis that the series is non-stationary is rejected
at 1% level of significance (critical Z test value equals to -3.43) for
all three variables and for both call and put options. We alternatively
conduct Phillips-Perron unit root test and find similar test statistics
as reported for ADF test.
Table 2 reports the contemporaneous regression results for both
call and put options. We find that the total volume, for both call and
put options, is having significant negative effect on daily-implied
volatility during recovery period. This implies that an increase in
options trading reduces the expected future volatility of Nifty spot
index during recovery period and is consistent with Sarwar (2005). The
COI is also found to be negatively affecting the implied volatility
during recovery period. However, we find COI is not significant in the
case of call options. These results suggest that in general arbitragers
and other market players operate actively in Nifty index options market
due to which significant portion of volatility related information is
impounded in the two markets simultaneously.
The volume and COI are also interacted with Uptrend and Downtrend
dummies to test if the relationship is consistent across market trends.
The coefficients of total volume for call options during both Uptrend
and Downtrend periods turn out to be positive and significant. This
implies that the effects of volume during Up and Down periods
significantly differ from the Recovery period. The overall impact of
call options volume during Up ([[beta].sub.11] + [[beta].sub.12]) and
Down periods ([[beta].sub.11] + [[beta].sub.13]) turns out to be
positive meaning an increase in call options trading increases the
expected value of spot market future volatility. COI for call options is
not having significant impact on volatility and this remains consistent
across trends.
The impact of volume in the case of put options is also found to be
significantly different from recovery period however, the overall impact
is positive during Uptrend and negative during Downtrend. COI of put
options is found to be having negative impact on volatility during
recovery period and is significantly different only from that of Up
period. Moreover, the overall impact during Up period is still negative
though, the magnitude changes from 0.004% to 0.001%. Results of COI for
both call and put options imply that a positive change in the open
interest indicates a fall in expected future volatility. Overall, the
options trading activity and volatility are found to be instantaneously
related. However, the magnitude of adjustment to information differs
across market trends. Our regression equation (1) explains a significant
proportion of total variance in expected future volatility (22.4% and
35.4% for call and put options respectively) and the VIFs of the
variables in the regressions remain below 2 indicating no
multi-collinearity among independent variables.
Table 3 presents the result of TVAR that test for direction of
information flow between spot and options markets. We report the sign
and significance of the parameters estimated through equation (2) (7).
We observe a significant impact of own lag/s in all three regressions
for both call and put options except for call options volume (Total_vol)
during Down period. It suggests that the own lag/s of the variables
is/are prominent predictor/s.
We find from put options results, that the total volume is
significantly affecting the implied volatility till two lags during
Aggregate and Up periods but with alternate signs. This implies that
volatility initially falls with a rise in options volume but then rises
on the subsequent day, which is consistent with under-reaction
hypotheses in literature. We find that during the Down period, the
volume is not having significant effect on volatility however, during
recovery period the second lag of volume is found significant. The
consistent alternate sign of coefficients strongly supports the
under-reaction hypothesis where volatility first undershoots and then
subsequently adjusts upward. The significant lagged put options volume
supports the volatility information related trading of Nifty Index put
options.
The impact coefficient of total COI on implied volatility for put
options is having alternate sign but only second lag is positive and
significant during Aggregate and Up periods. During Downtrend, the
impact of COI is positive for both lags but only first lag affects
significantly. No significant relationship between COI and volatility is
observed during Recovery period. We observe that COI affects volatility
on (t + 2) day during aggregate and up periods where t is the
transaction day. The consistent results during aggregate and up periods
are possibly due to total period of study largely overlapping with up
period. During down period COI affects volatility till next day only. We
observe that volatility related information from COI is transmitted
faster during Downtrend compared to that of Uptrend.
The impact of put options implied volatility on both total volume
and COI from Table 3 suggests the following: During aggregate period the
first two lags of implied volatility have significant impact on volume
with alternate signs showing under-reaction. However, during up period,
though the sign of coefficients remain consistent, only second lag is
found affecting positively and significantly. During Down and Recovery
periods the sign of the lag coefficients remain positive but
insignificant. The implied volatility is affecting the COI significantly
till two lags during Recovery period and the alternate signs of
coefficients indicate that with rise in volatility the COI increases
first but, on subsequent day it falls indicating an overreaction effect.
No significant impact of volatility is found on COI during Up and Down
periods however, the aggregate impact is found to be positive for both
lags, significant only for lag 2.
The results of Call options in Table 3 indicate that impact of
total volume on volatility is not significant at 5% level across periods
of study. The signs of lag coefficients are alternate consistently.
Unlike volume, the COI is having positive and significant effect during
up period. This suggests that the volatility informed traders do not
primarily use call options to trade on their information. Call options
implied volatility is not affecting volume too across periods of study
however, it affects COI significantly during down period till three lags
which, indicates hedge related use of call options during downtrend. The
first lag of volatility is also negative and significant during up
period. Volume and COI are found predicting each other significantly in
many instances, as expected, due to both being measures of options
market trading activities. Nevertheless, these results are not
highlighted as this study addresses different issue.
The results of TVAR for different classes of options moneyness are
reported in Table 4. We find that the total volume for put options has
positive and significant impact on implied volatility for OTM and ITM
options with the lag of one day. COI does not have significant effect on
volatility. Implied volatility also has significant impact either on
volume or on COI across moneyness classes.
Results for Call options show that an increase in options volume
results in rise of expected volatility the next day but is significant
only for OTM options enforcing volatility information based trading of
Nifty call OTM options. The implied volatility is also affecting the
total volume till two lags with alternate signs but only for OTM
options. This indicates the overreaction in trading OTM call options on
the expectation of increase in future volatility and points the hedging
role of OTM call options. COI for call options is not found affecting
volatility across moneyness classes however; volatility is found
affecting the COI significantly for ATM options. The results for call
options indicate the feedback relationship between the two markets for
OTM options making them preferred instruments for both informed traders
and hedgers.
Conclusions
The study investigates the dynamic relationship between future
volatility of S&P CNX Nifty Index and trading activity of Nifty
options. Two alternative measures of trading activity i.e. trading
volume measured by aggregate number of contracts traded and changes in
open interest, are considered in the study. We examine both
contemporaneous and lead lag relationship between expected volatility
and options trading activity and also analyse the relationship
separately for different market trends and options moneyness for both
call and put options.
The contemporaneous regression results show that options volume is
significantly related with future volatility and it is consistent across
market trends for both call and put options. The positive relationship
between volume and volatility can be attributed to shift of liquidity
from the spot market to the options that result into increase in the
options volume and the spot market volatility. Moreover, our results are
also consistent with the theoretical relationship of volatility with
options prices.
We also find that COI is related with volatility only in the case
of put options but turns out insignificant during Downtrend. Moreover,
when data post January, 2011 (relatively smaller downtrend) is dropped
from analysis, COI is found to be significantly affecting volatility
only during Up period. This suggests COI as a contemporaneous predictor
only in good times. The lead lag relationship based on TVAR model
suggests the predictability of options trading activities for future
volatility indicting volatility informed trading in options. However,
feedback relationship is also observed in few cases suggesting both
information and hedge based use of Nifty options. When options are
classified based on moneyness, we find OTM call options are the most
prominent contracts preferred by both informed traders and hedgers. The
sign and significance of the coefficients vary with varying market
trends and options moneyness suggesting that trader's preference
changes with changing market environment.
Based on our empirical analysis the main findings can be
highlighted as follows:
--The options in India have both the information based and the
hedging based uses which is consistent with the leverage (information
based trading) and the liquidity (hedge related trading) hypotheses.
--OTM options contracts are the most preferred options class for
trading by both informed traders and hedgers in Indian market.
Although this study considers two important factors, i.e. options
moneyness classes and market trends to examine the dynamic relationship
between the spot and the options markets yet, other factors such as
options liquidity, time to maturity can be considered to extend the
study further. As this study uses index options data, the results are
more appropriate for trading based on market wide information. A study
on component stocks using stock options contracts may help to know the
venue of informed trading in terms of idiosyncratic information about
firms.
http://dx.doi.org/10.3846/btp.2015.559
Rajesh PATHAK
Department of Finance and Accounting, IBS-Hyderabad, IFHE,
Dontanpally, RR District, Telangana 501203, India
E-mail: rpathak@ibsindia.org
Received 02 December 2014; accepted 23 February 2015
Acknowledgements
I am thankful to Dr. V. Nagi Reddy for his valuable comments and
suggestions on the methodology employed for the study that helped
immensely in improving on the analysis of the paper.
References
Beckers, S. 1981. Standard deviations implied in option prices as
predictors of future stock price variability, Journal of Banking &
Finance 5(3): 363-381. http://dx.doi.org/10.1016/0378-4266(81)90032-7
Bhattacharya, M. 1987. Price changes of related securities: The
case of call options and stocks, Journal of Financial and Quantitative
Analysis 22(1): 1-15.
Black, F. 1975. Fact and fantasy in the use of options, Financial
Analysts Journal 36-72. http://dx.doi.org/10.2469/faj.v31.n4.36
Canina, L.; Figlewski, S. 1993. The informational content of
implied volatility, Review of Financial studies 6(3): 659-681.
http://dx.doi.org/10.1093/rfs/5.3.659
Chakravarty S.; Gulen H.; Mayhew S. 2004. Informed trading in stock
and options market, The Journal of Finance 49(3): 1235-1257.
Chan, K. C.; Chang, Y.; Lung, P. P. 2009. Informed trading under
different market conditions and moneyness: Evidence from TXO options,
Pacific-Basin Finance Journal 17(2): 189-208.
http://dx.doi.org/10.1016/j.pacfin.2008.02.003
Chan, K.; Chung, Y. P.; Fong, W. M. 2002. The informational role of
stock and option volume, Review of Financial Studies 15(4): 1049-1075.
http://dx.doi.org/10.1093/rfs/15.4.1049
Chan, K.; Chung, Y. P.; Johnson, H. 1993. Why option prices lag
stock prices: a trading-based explanation, The Journal of Finance 48(5):
1957-1967. http://dx.doi.org/10.1111/j.1540-6261.1993.tb05136.x
Chang, C. C.; Hsieh, P. F.; Wang, Y. H. 2010. Information content
of options trading volume for future volatility: evidence from the
Taiwan options market, Journal of Banking & Finance 34(1): 174-183.
http://dx.doi.org/10.1016/j.jbankfin.2009.07.015
Chen, C. R.; Lung, P. P.; Tay, N. S. 2005. Information flow between
the stock and option markets: where do informed traders trade?, Review
of Financial Economics 14(1): 1-23.
http://dx.doi.org/10.1016/j.rfe.2004.03.001
Chen, N. F.; Cuny, C. J.; Haugen, R. A. 1995. Stock volatility and
the levels of the basis and open interest in futures contracts, The
Journal of Finance 50(1): 281-300.
http://dx.doi.org/10.1111/j.1540-6261.1995.tb05174.x
Chiras, D. P.; Manaster, S. 1978. The information content of option
prices and a test of market efficiency, Journal of Financial Economics
6(2): 213-234. http://dx.doi.org/10.1016/0304-405X(78)90030-2
Easley, D.; O'Hara, M.; Srinivas, P. S. 1998. Options volume
and stock prices: evidence on where informed traders trade, The Journal
of Finance 53(2): 431-465. http://dx.doi.org/10.1111/0022-1082.194060
Koch, P. D. 1993. Reexamining intraday simultaneity in stock index
futures markets, Journal of Banking & Finance 17(6): 1191-1205.
http://dx.doi.org/10.1016/0378-4266(93)90020-E
Kyriacou, K.; Sarno, L. 1999. The temporal relationship between
derivatives trading and spot market volatility in the UK: Empirical
analysis and Monte Carlo evidence, Journal of Futures Markets 19(3):
245-270. http://dx.doi.org/10.1002/(SICI)1096-9934(199905)19:3
<245::AID-FUT1>3.0.CO;2-J
Latane, H. A.; Rendleman, R. J. 1976. Standard deviations of stock
price ratios implied in option prices, The Journal of Finance 31(2):
369-381. http://dx.doi.org/10.1111/j.1540-6261.1976. tb01892.x
Mayhew, S.; Stivers, C. 2003. Stock return dynamics, option volume,
and the information content of implied volatility, Journal of Futures
Markets 23(7): 615-646. http://dx.doi.org/10.1002/fut.10084
Ni, S. X.; Pan, J.; Poteshman, A. M. 2008. Volatility information
trading in the option market, The Journal of Finance 63(3): 1059-1091.
http://dx.doi.org/10.1111/j.1540-6261.2008.01352.x
Pan, J.; Poteshman, A. M. 2006. The information in option volume
for future stock prices, Review of Financial Studies 19(3): 871-908.
http://dx.doi.org/10.1093/rfs/hhj024
Sarwar, G. 2005. The informational role of option trading volume in
equity index options markets, Review of Quantitative Finance and
Accounting 24(2): 159-176. http://dx.doi.org/10.1007/s11156-005-6335-0
Shaikh, I.; Padhi, P. 2014. Stylized patterns of implied volatility
in India-a case study of NSE Nifty Options, Journal of Indian Business
Research 6(3): 231-254. http://dx.doi.org/10.1108/JIBR-12-2013-0103
Stephan, J. A.; Whaley, R. E. 1990. Intraday price change and
trading volume relations in the stock and stock option markets, The
Journal of Finance 45(1): 191-220.
(1) (Bhattacharya 1987; Stephen and Whaley 1990; Chan et al. 1993;
Easley et al. 1998; Chan et al. 2002; Chakravarty et al. 2004; Chen et
al. 2005; Chang et al. 2010; Pan and Poteshman 2006)
(2) They define basis as the difference between the market futures
price and fair futures price where fair futures price is cash price
index grossed up by risk free rate and adjusted for expected dividends.
(3) Vega shows the sensitivity of options prices to changes in the
volatility of the underlying assets. Vega is most sensitive for
at-the-money options.
(4) Straddle is an option trading strategy where a trader buys a
call and sells a put with same strike price and maturity.
(5) We drop intercept dummy terms of Uptrend and Downtrend from
Equation (1) due to them having a Variance Inflation factor (VIF)
exceeding 5 when included in the regression equation. However, we test
if common implied volatility (CIV) are different during the sub-periods
defined as Uptrend, Downtrend and Recovery period by running a separate
dummy variable regression model with intercept and find the CIV to be
significantly different across trends at less than 1% level of
significance.
(6) The Shapiro-Wilk test is also conducted to test the null
hypotheses that the sample data comes from normally distributed
population. The W statistics is found to be lower however, the p-values
for every variable are found to be significant which rejects the null
hypothesis of normality.
(7) Coefficient estimates of the same are available on request.
Rajesh PATHAK, Dr., is an assistant professor at IBS-Hyderabad
(Icfai Foundation of Higher Education) in department of Accounting and
Finance. His research interests include equity derivatives and its
roles, price discovery and corporate finance. He teaches undergraduate,
graduate, and executive courses in finance and allied areas such as
accounting for managers, management accounting, financial risk
management, security analysis and portfolio management, financial
management, strategic financial management etc.
Caption: Fig. 1. Daily close value of S&P CNX Nifty 50 index
Table 1. Summary statistics of S&P CNX Nifty index options
(Aggregate)
Estimates Call options
Common_impvol Total_vol. Total_COI
(in Lakh.) (in lakh.)
Mean 0.237 4.621 10.898
Median (p50) 0.219 1.234 5.585
S.D 0.088 6.188 25.514
Max 1.377 38.387 747.508
Min 0.058 0.012 -64.657
Std. Error (mean) 0.002 0.141 0.582
Skewness 2.286 1.744 14.582
Kurtosis 19.327 6.015 380.644
ADF Test stats. -16.39 -7.43 -30.2
Estimates Put Options
Common_impvol Total_vol. Total_COI
(in Lakh.) (in lakh.)
Mean 0.008 4.686 12.257
Median (p50) 0.006 1.334 6.955
S.D 0.009 6.191 18.530
Max 0.266 36.090 216.741
Min 0.000 0.007 -88.734
Std. Error (mean) 0.000 0.141 0.423
Skewness 13.057 1.647 2.278
Kurtosis 333.293 5.492 16.919
ADF Test stats. -27.67 -6.19 -24.56
Note: Table 1 presents the summary statistics of important
variables from the study for call and put options separately.
Common_impvol represent estimated common implied volatility
measured Vega weighted average of implied volatility of
options. Total_vol. (in Lakh.) shows the turnover whereas
Total_COI represent the total changes on open interest.
We report first four moments namely mean, standard deviation
(S.D), Skewness and Kurtosis along with positional average
median (the 50th percentile or p50). The highest and lowest
observation value and the statistics for stationarity test
(ADF test) are also reported. The negative value (in italics)
of Total_COI (in lakh) variable indicates negative changes in
open interest meaning excess of closure of outstanding positions
compared to new positions. The number of observations is 1922
in all cases for both call and put options.
Table 2. Contemporaneous regression results
Category Total Total COI Up Total Down Total
Volume Vol Vol
Call -0.0013 *** -4.7E-05 0.0092 *** 0.0213 ***
Options (-3.92) (-0.35) (5.38) (17.59)
Put -0.0004 *** -3.0E-05 ** 0.0034 *** -0.0003 **
Options (-11.78) (-2.67) (8.86) (-2.25)
Category Up COI Down Cons. [R.sup.2]
COI
Call -0.0001 0.0003 0.2263 *** 0.2243
Options (-0.68) (1.12) (97.40)
Put 0.0003 *** 3.1E-05 0.0083 *** 0.3544
Options (10.51) (1.18) (33.53)
Note: **, *** represent the significance of coefficients at 5%
and 1% levels. Table 2 shows the contemporaneous regression
results for call and put options where estimated coefficients
of explanatory variables i.e. total volume, total COI and
their interaction with up and down dummies, are reported along
with their t-statistics in parenthesis. [R.sup.2] of the
regressions are shown in the last column and the number of
observations in each of the regressions is 1922.
Table 3. Results of TVAR for aggregate period
and sub-periods (Up, Down and Recovery)
Dependent Lag All
Variable Variable
Lag1 Lag2 Lag3
Put Options
Imp_Vol Imp_Vol + *** + *** NA
Total_Vol - ** + ** NA
COI - + ** NA
Total_Vol Imp_Vol - ** + ** NA
Total_Vol + *** + *** NA
COI + + *** NA
COI Imp_Vol + + ** NA
Total_Vol - *** + *** NA
COI + *** + *** NA
Call Options
Imp_Vol Imp_Vol + *** + *** +
Total_Vol + * - +
COI + * + -
Total_Vol Imp_Vol + - +
Total_Vol + *** + + ***
COI + + + *
COI Imp_Vol - + * +
Total_Vol - + +
COI + *** + _**
Dependent Lag Up
Variable Variable
Lag1 Lag2 Lag3
Put Options
Imp_Vol Imp_Vol + *** + *** NA
Total_Vol _*** + *** NA
COI - + ** NA
Total_Vol Imp_Vol - + ** NA
Total_Vol + *** + *** NA
COI - - NA
COI Imp_Vol + + NA
Total_Vol -* + *** NA
COI + *** + NA
Call Options
Imp_Vol Imp_Vol + *** + ** + **
Total_Vol + * - +
COI + ** + +
Total_Vol Imp_Vol + + -
Total_Vol + + * +
COI + *** - -
COI Imp_Vol - ** - + **
Total_Vol - - + ***
COI + *** + - ***
Dependent Lag Down Rec
Variable Variable
Lag1 Lag2 Lag3 Lag1 Lag2
Put Options
Imp_Vol Imp_Vol + *** + *** NA + *** + ***
Total_Vol - + NA - + **
COI + ** + NA + -
Total_Vol Imp_Vol + + NA + * +
Total_Vol + *** + * NA + *** + ***
COI + + NA - +
COI Imp_Vol + - NA + *** - **
Total_Vol + + NA - * + ***
COI + *** - NA + *** + **
Call Options
Imp_Vol Imp_Vol + ** + *** - + *** - **
Total_Vol + * - + - +
COI + - - + -
Total_Vol Imp_Vol - * + + * + * -
Total_Vol + + + + *** + ***
COI + + + - +
COI Imp_Vol - ** + *** - + +
Total_Vol - * + - - + ***
COI + *** + - + *** +
Table 4. TVAR results for different classes of options moneyness
Category Dependent Lag ATM OTM
Variable Variable
Lag1 Lag2 Lag1 Lag2
Put Imp_Vol Imp_Vol + *** + *** + *** + ***
Options Total_Vol + - - + ***
COI + * - + - *
Total_Vol Imp_Vol + - + +
Total_Vol + *** + *** + *** + ***
COI + + *** + *** -
COI Imp_Vol + * - + +
Total_Vol - + *** - *** + ***
COI + *** + *** + *** + ***
Call Imp_Vol Imp_Vol + *** + *** + *** + ***
Options Total_Vol + + + ** -
COI - + + +
Total_Vol Imp_Vol + + + ** - **
Total_Vol + *** + *** + *** + ***
COI - *** + + ** - **
COI Imp_Vol - * + *** + * -
Total_Vol + + *** - *** + **
COI + + * + *** +
Category Dependent Lag ITM
Variable Variable
Lag1 Lag2
Put Imp_Vol Imp_Vol + *** + ***
Options Total_Vol - + ***
COI + +
Total_Vol Imp_Vol - +
Total_Vol + *** +
COI + ** -
COI Imp_Vol - +
Total_Vol - *** - ***
COI + *** - ***
Call Imp_Vol Imp_Vol + *** + ***
Options Total_Vol + +
COI - +
Total_Vol Imp_Vol + +
Total_Vol + *** + ***
COI + *** +
COI Imp_Vol + +
Total_Vol - *** +
COI + * + **
Note: *** is p < .01, ** is p < .05 and * is p < .10: Here
Options moneyness categories ATM, OTM and ITM are At-the-Money,
Out-of-the-Money and In-the-Money options. Imp_vol indicates
daily common implied volatility (CIV), Total_vol indicates total
number of contracts traded daily across series of options. COI
represents daily aggregate changes in open interests across
series of options. Lag lengths are determined based on AIC
criterion.
