Academic journal article IUP Journal of Applied Finance

Forecasting Performance of Volatility Models for Pricing S&P CNX Nifty Index Options Via Black-Scholes Model

Academic journal article IUP Journal of Applied Finance

Forecasting Performance of Volatility Models for Pricing S&P CNX Nifty Index Options Via Black-Scholes Model

Article excerpt

(ProQuest: ... denotes formulae omitted.)

Introduction

Since the seminal work of Black-Scholes in 1973, the study of volatility has become the most active area of modern finance. Previous empirical research work of practitioners proved that for replication of actual volatility, limited sample time of asset return was enough. While empirical performance of m-windowed moving average and historical volatility (standard deviation) models also provide the evidence for the same, it is windowed moving average volatility model which always leads. Volatility can be measured in two ways: implied volatility, which is forward looking, reflects the volatility of the underlying asset given its market's option price; and the other way is historical volatility which is backward looking.

Innovations in volatility estimation, such as stochastic volatility and autoregressive conditional heteroskedasticity, have tried to integrate well-known observed properties of volatilities like skewness, volatility clustering and mean reversion into models (see Nelson, 1991; Pagan, 1996; and Bekaert and Wu, 2000). As a result of continuing innovations and rapid transformation in the volatility modeling landscape, new concepts continue to appear; some of them are more effective than benchmark Black-Scholes model but appear more complex than it too.

Although recent innovations in volatility forecasting were catalysts for improvements in the estimation process, they have proven to complicate model building as a whole. For instance, new parameters have to be calculated. However, Pagan and Schwert (1990), Poon and Granger (2003), Alberg et al. (2008) and Floros (2008) reported that implied volatility estimators performed better than historical and GARCH type estimators. Along these lines, we compared forecasting performance of implied and time series econometric volatility models by incorporating them in the Black-Scholes model.

The success of the Black-Scholes formula is mainly due to the possibility of synthesizing option prices through a unique parameter, the implied volatility, which is so crucial for traders to be directly quoted in many financial markets. Historical analysis shows that volatilities are indeed stochastic, often correlated with the underlying asset price (see Dumas et al., 1998). Stochastic volatility models, therefore, seem to represent a more realistic choice when modeling asset price dynamics for valuing derivative securities. However, only a few studies retain enough analytical tractability. But calibration of stochastic models is extremely burdensome and time-consuming (see Hull and White, 1987; Heston, 1993; and Heston and Nandi, 2000).

The aim and objective of this paper is to forecast performance of volatility models for pricing S&P CNX Nifty index options via Black-Scholes model incorporating implied volatility, VIX and GARCH class volatility as inputs.

Data and Methodology

Data

This study employs historical data of S&P CNX Nifty 50 index, Nifty option contract and the Indian "risk-free" interest rate data which is equal to the yield of 91-Day T-Bill.1 The data consist of closing price records from January 1, 2008 to December 31, 2008, obtained from NSE.2 For the option contracts, the date, time, contract month, option type, strike price, and traded prices were obtained.

Data Screening Procedure

Data screening procedure and methodology displayed here are akin to Singh and Ahmad (2011, p. 89). We have deployed three exclusionary filters to the collected market option prices data for filtering the relevant data to compare and contrast volatility models. First, option strike prices with maturity greater than 90 days are excluded as they remain less actively traded on NSE. Second, all the call option prices taken from the market are checked for the lower boundary condition:

...

where St is the current asset price, K is the strike price, q is the continuous compounded dividend yield of the asset, r is the risk-free interest rate, C(St, t) is the call price at time t, and T - t is the time to maturity. …

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