An Option Valuation Formula for Stochastic Volatility Driven by GARCH Processes

Abstract

We have developed a practical and elegant closed-form option pricing formula for general GARCH models using a risk-neutral argument. To estimate the parameters, we propose a procedure and utilize Monte Carlo simulation to calculate the prices. Our formula has been successfully applied to S&P 500 index options and Chinese SSE 50 ETF options, providing empirical evidence that it outperforms the Black-Scholes formula with constant volatility in both the U.S. and Chinese financial markets. While there may be other equivalent martingale measures in this setting, our formula serves as a useful reference for pricing options.