An Application of GARCH Models in Detecting Systematic Bias in Options Pricing and Determining Arbitrage in Options

Abstract

Derivatives have become widely accepted as tools for hedging and risk-management, as well as speculation to some extent. A more recent trend has been gaining ground, namely, arbitrage in derivatives.

The critical parameter in derivatives pricing is the volatility of the underlying asset. Exchanges often overestimate volatility in order to cover any sudden changes in market behavior, leading to systematic overpricing of derivatives. Accurate forecasting of volatility would expose systematic overpricing. Unfortunately, volatility is not an easy phenomenon to predict or forecast. One class of models that have proved successful in forecasting volatility in many situations is the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) family of models.

The objective of the present study is to analyze systematic bias in the pricing of options derivatives. In order to perform the analysis, data were collected for a sample of stock options traded on the National Stock Exchange (NSE) of India and their underlying stocks. In the study, GARCH models are used to forecast underlying stock volatility, and the forecasted volatility is used in the Black-Scholes model in order to determine whether the corresponding options were fairly priced. Any systematic bias in options pricing would provide evidence for arbitrage opportunities.

Keywords: derivatives, hedging, speculation, arbitrage, volatility, overpricing, GARCH, Black-Scholes model

JEL Classification: G13