CHAPTER VI
SUMMARY, CONCLUSION AND POLICY
IMPLICATIONS
Securities markets in the past 20 years have seen the emergence of an astonishingly theoretical approach to valuation, market making, and arbitrage in complex market sectors. Many securities firms now base their bid and offer prices for complex securities on detailed analytic or computer models built by scientists. Most of this theory centres on derivatives, instruments whose value stems from their contractually defined relation to more elementary securities or market parameters. In this generalized sense, derivatives encompass many products: futures and options are derivatives on the underlying index and stock, collateralized mortgage obligations (CMOs) are derivatives on interest and prepayment rates and even regard bonds are derivatives on interest rates.
In India, financial market liberalization since early 1990’s has brought major changes in the financial system of our country. The creation and empowerment of Securities and Exchange Board of India (SEBI) has helped in providing higher level accountability in the market. New institutions like National Stock Exchange of India (NSE), National Securities Clearing Corporation (NSCCL), and National Securities Depository (NSDL) have been the change agents and have helped cleaning the system and provided safety to investing public at large. With modern technology in hand, these institutions
have set benchmarks and standards for others to follow. The microstructure changes brought about reduction in transaction cost that helped investors to lock in a deal faster and cheaper. The major changes in the capital market have resulted in the complete transformation of structure and composition of the market. In addition Indian capital markets also have started trading on derivative products in line with the developed countries.
Basically, a derivative is a product whose value is derived from the value of one or more basic variables called bases in a contractual manner. The underlying asset can be equity, commodities, interest rate or any other asset. The price of a derivative is contingent to the price of its underlying asset. Futures and Options are the different variants of derivative contract which are traded on exchanges, and they are standardized according to the rules and regulations of the exchange.
In India, the introduction of derivatives in its capital market started with Securities Exchange Board of India (SEBI) sets up with a 24 member committee under the chairmanship of Dr. L. C. Gupta on November 18, 1996 to develop appropriate regulatory framework for derivatives trading in India. The committee submitted its report on March 17, 1998, prescribing necessary pre-conditions for the introduction of derivatives trading in India. The committee recommended that derivatives should be declared as “securities” so that regulatory framework applicable to trading of “securities” could also
govern trading of securities. SEBI also set up a group in June 1998 under the Chairmanship of Prof. J. R. Varma, to recommend measures for risk containment in derivatives market in India. The report, which was submitted in October 1998, worked out the operational details of the functioning of derivative market in terms of margining system, methodology for charging initial margins, broker net worth, deposit requirement, real - time monitoring requirements, etc.
In India, the derivatives trading commenced in June 2000 after Securities Exchange Board of India (SEBI) granted the final approval to this effect in May 2001. SEBI permitted the derivative segment in two stock exchanges i.e. NSE and BSE. Trading first commenced in Index futures contracts, followed by index options in June 2001, options in individual stocks in July 2001, futures in single stock derivatives in November 2001 and the interest rate futures in March 2003. NSE also introduced trading in futures and option contracts based on CNX-IT index and CNX Bank Nifty in August 2003 and June 2005 respectively. In June 2007, NSE launched its trading on futures and options on CNX 100 and CNX Nifty Junior indices. In January 2008, NSE initiated Mini derivative (Futures & Options) contracts on Nifty. In March 2008, NSE also launched long term option contracts on S&P CNX Nifty index. Derivative contracts on DEFTY index were introduced in December 2008. Nifty Junior, CNX 100 and DEFTY indices were discontinued from option trading from July 31, 2009.
India’s experience with the launch of equity derivatives market is extremely positive. The derivatives turnover on the NSE has surpassed the equity market turnover. The turnover of derivatives on the NSE increased from Rs. 23,654 million (US $ 207 million) in 2000-01 to Rs. 177,193,220 million (US $ 36,817 million) in 2009-10. As per details presented in World Federation of Exchanges (WFE) Annual Report and Statistics 2010, NSE held the second position in terms of number of single stock futures and stock index options contracts traded in 2010. It was third in terms of number of stock index future contracts traded in 2010.
The estimation of the variance of the return on an asset is a crucial issue in modern applied finance. Volatility was first introduced into the financial world in Markowitz (1952) mean-variance model of portfolio selection. It was later demonstrated to play a crucial role in option pricing in the Black-Scholes (1973) model. The present research work has been developed on the background of earlier studies attempted in this area. Since Black & Scholes published their seminal article on option pricing in 1973, there has been an explosion of theoretical and empirical work on option pricing. Among most option pricing models, volatility, associated with risk and uncertainty, it has become one of the key inputs and has deservedly attracted the attention of both academics and practitioners. In the field of empirical option pricing, many studies have concentrated on the volatility implied the option’s market price based on an option pricing model.
In the framework of the Black-Scholes model, an equilibrium option price is a function of five variables: The current stock price, the time to maturity of the option, the exercise price, the risk free interest rate, and the volatility of the return of the underlying stock. Among these variables volatility is the only unobservable one. Historical stock price data may be used to estimate the volatility parameter, which then can be plugged into the option pricing formula to derive option values. As an alternative, once an option price is observed from the market, one can solve the Black-Scholas formula backward to obtain the volatility implied in this option price. This volatility is called implied volatility.
The option-pricing model derived by Black and Scholes(BS) is a path breaking work in the area of contingent claim pricing. When market prices are used to estimate implied volatilities, the smile effect has been spotted early by Black and Scholes in their empirical work on comparing market warrant prices to theoretical prices. The pattern of implied volatility for different time to maturity is known as the term structure of implied volatility, and the pattern across strike prices is known as the volatility smile or the volatility sneer. The term of volatility structure is used generally to refer to the pattern across both strike price and time to maturity. Many studies such as Black (1975), Macbeth and Mervulle (1979), and Rubinstein (1985, 1994) report empirical evidence of smile structure which has been identified in different markets. Shastri and Wethyasvivorn (1987) found that there was no unique implied volatility pattern
with respect to option maturity. Sheik (1991) followed the non-parametric approach of Rubinstein (1985) and found U-Shaped pattern on S&P 100 call option, which was often characterized as a ‘smile pattern’. Fung and Hsieh (1991) conducted an empirical analysis of implied volatilities across three futures option markets and found that the smile pattern is more pronounced for the Deutschemark futures options. Heynen (1993) observes smile pattern to be inconsistent in European Options Exchange and suggests an alternative explanation for the volatility smile, based on market imperfections. Taylor and Xu (1994) observed asymmetric pattern while studying the options on stock index futures listed on Chicago Mercantile Exchange (CME). While Duque and Paxson (1994) found the smile effect for options traded on LIFFE, Bakshi et al. (1997) reported that Black-Scholes implied volatility exhibits a clear U-shaped pattern across moneyness, with the most distinguished smile evident for options near expiration. Dumas, Fleming and Whaley (1998) reported empirical smiles for options on S&P 500 Stock Index. Peria, Serna and Rubio (1999) found smiles for stock index options written on Spanish index of IBEX 35. In Sydney Futures Exchange (SFE), Brown and Taylor (1997) and Brown (1999) observed smile in the implied volatilities. Engstorm (2002), Duque and Lopes (2003) and Bollen and Whaley (2004) found empirical evidence for U-Shaped smiles.
In the Indian context, the study conducted by Verma (2002) reports the existence of mispricing and consequent volatility in the Indian Index options market. Misra, et al. (2006) have found that deeply in-the- money and deeply out-of-the-money options have higher implied volatility than at the money options, as well as it is higher for far the month option contracts than for near the month option contracts. Malabika Deo, Devanadhen and Srinivasan (2008) have examined the selected individual stock call option and found U-shaped smile pattern across moneyness and time to maturity.
Apart from the volatility structure, the relationship between the implied and realized volatility has to be investigated. Latane and Rendlemen (1976) are the first to examine 24 stocks options traded on Chicago Board Option Exchange (CBOE) and report that implied volatility is significantly correlated with actual volatility. In the light of this paper, Chiras and Manaster (1978), and Beckers (1981) used a large sample of CBOE stock options and discovered implied volatility is superior to historical volatility in forecasting realized volatility.
In dynamic background, later studies have focused on the information content of implied volatility. Day and Lewis (1992) and Canina and Figlewski (1993) report that implied volatility has no statistically significant correlation with realized volatility. Lamoureux and Lasptrapes (1993) used at-the-money implied volatility of CBOE call option and concluded that implied volatility was biased but informative, and historical volatility contributed additional
information in forecasting future stock return volatility. At this point of time, literature argues that volatility implied by option prices is biased and inefficient predictor of realized volatility, and does not outperform volatility obtained from historical information.
In contrast to the previous studies, Gemmill (1986, 1993) first examined the information content of implied volatility using U.K. data and concluded that implied volatility contains information about future volatility beyond that in the time-series forecast. Jorion (1995) examined the information content of implied volatility of foreign currency futures option on Chicago Mercantile Exchange (CME) and found implied volatility is an unbiased and informationally efficient forecast of realized volatility. Bates (1996) surveyed different weighting schemes to aggregate implied volatilities and concluded that no single alternative hypothesis about the underlying distribution can eliminate the found biases across exercise prices. Vasilellis and Meade (1996) demonstrated that implied volatilities produce better individual forecasts than time series. Fleming (1998) examined implied volatility of S&P 100 index and observed that index call and put options are biased, but the bias does not throw opportunities to earn economically significant profits. Gwilym and Buckle (1999) present evidence that implied volatility is biased but contains more information of future realized volatility than historical volatility. The above studies are based on overlapping datasets and suffer from the serial correlation problem, which leads to overstating the explanatory power.
To deal with this problem, Christensen and Prabhala (1998), Hansen and (2001), Christensen and Hansen (2002) introduced a non-overlapping data series i.e. one implied volatility to one realized volatility. They used instrumental variable method to correct the errors-in-variable problem in the measurement of implied volatility and concluded that implied volatility is unbiased and efficient in forecasting of future volatility. In the light of the above paper, Blair, Poon and Taylor (2001) concluded that nearly all relevant information is provided by the VIX index and hence there is not much incremental information in high-frequency index returns. Ederingtion and Guan (2002) examined OEX options market and suggested implied volatility has strong predictive power and generally subsumes the information in historical volatility. Claessen and Mittnik (2002) supported the efficient market hypothesis for the DAX-index options market. Shu and Zhang (2003) examined the relationship between realized and at-the-money implied volatility of S&P 500 index options traded on the CBOE and found that implied volatility is a biased estimator but outperforms historical volatility. Szakmary, et al. (2003) investigated 35 futures markets on eight separate exchanges and concluded implied volatility is not completely unbiased. Li and Yang (2008) examined the relationship between the volatility implied and realized volatility by using the S&P/ASX 200 index options (XJO) traded on the Australian Stock Exchange (ASX) and found that both call and put implied volatilities are superior to historical volatility in forecasting future realized volatility. Moreover, implied call volatility is nearly an unbiased forecast of future
volatility. Yu, Lui and Wang (2009) investigated the efficiency of stock index options traded over-the-counter (OTC) and on the exchanges in Hong Kong and Japan, and concluded that the OTC market is more efficient than the exchange in Japan, but that the opposite is true in Hong Kong. Taylor, Yadav and Zhang (2010) measured the volatility information content of stock options for individual firms, using option prices for 149 US firms and the S&P 100 index and found at-the-money implied volatilities generally outperform the model-free volatility expectations.
In contrast to previous studies, Goit (2002) demonstrated that volatility forecasts based on the VIX/VXN indices have the highest information content, both in the volatility forecasting and market risk assessment frameworks. Jiang and Tian (2005) concluded that the model-free implied volatility subsumes all information contained in the Black-Scholas implied volatility and historical volatility and is more efficient in the forecast of future realized volatility.
At the international level, there exist numerous studies on forecasting the efficiency of implied volatility, however only a limited attempt has been made in the Indian stock market. Rao (2005) suggested option markets inefficiency; it may be because of mis-specification of the volatility process in the option valuation model and /or the existence of early exercise market opportunities. Maheshwaran and Ranjan (2006) concluded that the implied volatility is a poor and biased estimator of realized volatility. Mohan and Chaturvedual (2008) reported that IMVI is a poor and biased estimator of
realized volatility. Kumar (2008) studied S&P CNX Nifty call and put options and proved that implied volatility outperforms the historical volatility in forecasting the future realized volatility. Panda, Swain and Malhotra (2008) examined the information content of call and put options and found implied volatility contains more information than historical volatility, but is slightly a biased estimator of realized volatility. Devanadhen and Rajagopalan (2009) reported that at-the-money implied volatility is upward biased and informationally efficient in predicting future realized volatility. Previous Indian studies fail to provide any strong evidence on volatility structure and relationship between implied and realized volatility because of small sample size, short study period and immaturity of market structure in the initial phase, and no attempt is made on stock options. Hence, the current study attempts to shed light on the volatility structure and forecasting efficiency of implied volatility of selected stock option in India to fill the gap in the existing literature.
On the above backdrop, the main objectives of the present study are; 1. To study the conceptual framework of derivatives and development of
derivatives market in India
2. To understand how the implied volatility is measured and the pattern of option value implied volatility across time and moneyness
3. To assess the information content of implied volatility and historical volatility towards realized volatility
4. To examine the implied volatility as an unbiased forecast of future realized volatility
5. To examine whether the implied volatility impounds all the relevant information of historical volatility to forecast the realized volatility.
The objectives of the study are evaluated in two phases; where phase-1 examines Volatility structure implied by the Indian option against moneyness and time left to maturity and Phase-2 covers forecasting efficiency of implied volatilities.
The study period spanned from January 2002 to June 2010 with a sample of S&P CNX Nifty option and selected five stock option contracts. Mumbai inter-bank offer rate (MIBOR) is used proxy for risk-free interest rate. The daily stock price is collected from equity market segment on the NSE website for the sample companies for the matching period. All the required information was collected from National Stock Exchange (NSE) and their contract specifications. Trading details were retrieved from their website terminal (www.nseindia.com). Implied call and put volatilities are calculated by using Black-Scholes-Merton Model. Implied volatilities are average across different groups of moneyness, to view the pattern of volatility. Furthermore, implied volatilities are average across moneyness and time left to maturity.
In phase-2, the relationship between implied volatility and realized volatility is examined. The study used non-overlapping at-the-money option contract with a time to maturity of 30 calendar days for S&P CNX Nifty option and selected five individual stock options of call and put during the period from January 1, 2002 to June 30, 2010. Annualized standard deviation of continuously compounded return for computing of historical and realized volatility is employed. Augmented Dickey Fuller (ADF) test and Phillips-Perron (PP) test are employed to check stationarity of the volatilities series. OLS regression is used to capture the relationship between implied volatility and realized volatility. Hausmen test is used to verify the existence of error-in-variable (EIV) problem. In order to overcome error-in-error-in-variable problem, Instrument variable method is used. Wald test is used to examine the unbiasedness of implied volatility. The data were analyzed by using the econometric software package e-views.
In Chapter III, the study discussed the concept and types of the derivatives and its instruments such as forwards, futures and options. A forward or futures contracts involves an obligation to buy or sell an asset at a certain time in future for a certain price called calls and puts, respectively. A call option gives the holder the right to buy an asset by a certain date for a certain price. Derivatives have been very successful innovations in capital markets. Three types of traders can be identified in these markets: hedgers, speculators and arbitragers. Hedgers are in the position where they face risk
associated with the price asset. They use derivatives to reduce this risk. Speculators wish to bet on future movements in the price of an asset. They use derivatives to get extra leverage. Arbitragers are in business to take advantage of a discrepancy between prices in two different markets. Significance of Indian derivative market, clearing and settlement mechanics, risk management system and margins are discussed in this chapter.
Chapter VI investigate the pattern of the volatility structure implied by S&P CNX Nifty option, and selected five individual stock options are illustrated. Pattern of implied volatility in accordance with moneyness exhibit U-shape, with lowest average implied volatility found for at-the-moneys. Deep in-the-money is higher than deep out-of-the-money implied volatilities for both call and put option. Further, pattern of the implied volatility against moneyness and time left to maturity is investigated. In accordance with time left to maturity, the implied volatility of deep in-the-money call options are higher than deep out-of-the-money for shorter time left to maturity. Implied volatility of deep out-of-the money call options are higher than deep in-the-money for longer time left to maturity. In case of put options, the shorter the time left to maturity, deep in-the-money options are higher than deep out-of-the-money. Longer the time left to maturity, the deep in-the-money options implied volatilities tend to decrease monotonically. The term structure of implied volatility is nearly flat of at-the-money call and put options, both more fluctuant for deep in-the-money and deep out-of-the-money options. This
finding is similar to Duque & Lopes (2003) that the change in smile shapes as time to maturity dies out. This may be seen as in support of the expected “wry grin” for long term options. But the “reverse grin” is deeply unexpected for short-term options. In fact, the maturity approach changes the options smile asymmetry, converting a “wry grin” typical for longer term series into a “reverse grin” for nearly expiring options, with a more or less symmetric smile in a three dimensional domain.
The findings of the analysis suggest that the Black-Scholes-Merton Model tends to overprice in-the-money call options and out-of-the-money put options and underprice in-the-money put option and out-of-the-money call options. This asymmetry may be an outcome of the violation of Black-Scholes-Merton model due to high transaction cost and restriction on short selling in the Indian context. At-the-money options are often most actively traded and hence they are less likely to be mispriced.
Chapter V investigates the relationship between implied volatility and future realized volatility of S&P CNX Nifty option and selected five individual stock options. This study is based on non-overlapping monthly data, which are constructed by a sampling procedure proposed by Christensen and Prabhala (1998). The initial results of the descriptive statistics demonstrate that mean put volatility is higher than call volatility, and standard deviation of put volatility is slightly more volatile than call volatility. According to Harvey and Whaley (1991, 1992), buying pressure on put option is larger than on call option
because put option is relatively inexpensive and convenient for hedging. Consequently, implied put volatility is higher than implied call volatility on average and standard deviations of put volatility are slightly more volatile. The historical volatility is higher than realized volatility and standard deviation of historical volatility is slightly more volatile than realized volatility. This may be due to the excess volatility on the expiration days, since the expiration day is excluded in the measurement of realized volatility while it is included in the measurement of historical volatility. The average implied call and put volatility are larger than the average realized and historical volatility for S&P CNX Nifty and selected four stock options (except SBI). Our finding indicates that Black-Scholes-Merton Model tends to overprice both at-the-money call and put option on average.
According to OLS method, it is found that implied call and implied put volatility subsumes all the information to predict the future realized volatility except SBI. In case of SBI, historical volatility includes all the information to forecast the future realized volatility. The implied volatilities of S&P CNX Nifty option are slightly biased and informationally efficient forecast of future realized volatility. Reliance call and put volatility, Infosys call volatility and ITC put volatility seem to be unbiased and informationally efficient forecast of future realized volatility. Remaining stock options are found to be biased. So the result of the study matches with Fleming’s (1998), who reports that α= 0 and β < 1 &P 100 OEX options. Furthermore, implied volatility has slightly higher predictive power than historical volatility. However, these results can be
misleading because of the presence of measurement errors in implied volatility, namely the errors-in-variable (EIV) problem.
Hausman (1978) test is performed and it formally confirms the existence of EIV problem in stock option which is biased. To account for this problem, an Instrument Variable (IV) method is utilised. It is found that implied volatility of individual stock option is unbiased and informationally efficient predictor of future realized volatility except SBI.
The finding of the analysis suggests that implied bias will persist only if it is difficult to perform arbitrage trades that may remove the mispricing. This is more likely in the case of S&P CNX Nifty options. Stock and options are traded in different markets. Since trading of a basket of stock is unmanageable, arbitrage trades in relation to a mispriced stock index option may have to be done indirectly.
Policy Implication from the Study:
1. The study observes that the option market increases the efficiency of the market by providing information to decision-makers and planners to cater to the needs of the market participants.
2. The finance managers, in Indian context, may rely on Black-Scholes-Merton models to predict future volatility of individual stock for the horizon of one month. But they should be cognizant of the observable limitations.
3. The stock exchanges and market regulator (SEBI) need to take certain initiatives in terms of extending the short-selling facility and start trading of volatility index (VIX) to enhance the accuracy of implied volatility forecasts.
Limitations of the Study:
The limitation of the data is based upon secondary source obtained from National Stock Exchange. The study focuses on the relationship between implied and realized volatility. The information content of implied volatility is limited to Black-Scholes-Merton pricing model. The other option pricing models like stochastic volatility model, Heston model, Model free implied volatility and Binomial model are not taken into account. Sample annualized standard deviation of continuously compounded return for computation of historical and realized volatility is employed. No other measure methods like
GARCH, EGARCH, GJR-GARCH, Parkinson (1980) volatility estimator and Yang and Zhang (2000) range-based volatility estimator are applied.
Broader and long term issues involving Foreign Institutional Investment, Foreign Direct Investment and Global Meltdown impact on India and their nationwide implications have not been discussed in this research. The thesis is limited to the period from January 2002 to June 2010. In spite of these limitations, it is hoped that the findings will be useful to identify the status for developing derivative markets.
Agenda for Further Research:
The results of this dissertation present several questions that deserve further research. Some of these issues relate directly to the option market volatility while others do not. So, an in-depth analysis is required at the international level between the developed and emerging markets, and it is an interesting area yet to be answered by the researchers for the investors’ community. Finally, several directions for future research could be investigated to improve the volatility behaviour of Indian financial market:
1. Tests of pricing efficiency using alternative option pricing models 2. Forecasting power of implied volatility can be tested with intraday high
frequency data.
3. Testing the net buying pressure which affects the shape of implied volatility functions
4. Tests of efficiency related to put call parity theorem and profitability of different option market strategies
5. Relationship between the behaviour of stock index options and stock index futures
6. Effectiveness in the use of options and other financial derivatives by financial institutions such as banks, which use options for hedging risks 7. Information content of model free implied volatility
