GARCH Models for Forecasting Volatility and Determining Arbitrage in Options

Derivatives have become widely accepted as tools for hedging and risk-management, and also to some extent for speculation. A more recent trend has been gaining some ground, that of arbitrage in derivatives.The critical parameter in derivatives pricing is the volatility of the underlying asset. Exchanges often overestimate volatility in order to cover for any sudden changes in market behavior, leading to systematic overpricing of derivatives. Accurate forecasting of volatility would expose this systematic overpricing.Unfortunately, volatility is not an easy phenomenon to predict or forecast. One class of models which have proved successful in forecasting volatility in many situations is the GARCH family of models. The objective of the present study is to analyze systematic mispricing of options derivatives. In order to perform the analysis, data was collected for a sample of NSE-traded stock options and for their underlying stocks for the period of one year prior to the contract. The study uses GARCH models to forecast underlying stock volatility, and uses this forecasted volatility in the Black-Scholes model in order to determine whether the corresponding options are fairly priced. The motivation behind the research was to find systematic mispricing that would provide evidence for arbitrage opportunities