%0 Journal Article
%T An Option Valuation Formula for Stochastic Volatility Driven by GARCH Processes
%A Zhongmin Qian
%A Xingcheng Xu
%J Journal of Mathematical Finance
%P 221-247
%@ 2162-2442
%D 2023
%I Scientific Research Publishing
%R 10.4236/jmf.2023.132015
%X 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.
%K Option Pricing
%K Stochastic Volatility
%K GARCH
%K Risk Premia
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=125383