Pricing and Hedging Index Options under Stochastic Volatility: An Empirical Examination

Abstract:     
An empirical examination of the pricing and hedging performance of a stochastic volatility (SV) model with closed form solution (Heston 1993) is provided for options on the S&P 500 index in which the unobservable time varying volatility is jointly estimated with the time invariant parameters of the model. Although, out-of-sample, the mean absolute pricing error in the SV model is always lower than in the Black-Scholes model, still substantial mispricings are observed for deep out-of-the-money options. The degree of mispricing in different options classes is related to bid-ask spreads on options and options trading volume after controlling for moneyness and maturity biases. Taking into account the transactions costs (bid-ask spreads) in the options market and using S&P 500 futures to hedge, it is found that the stochastic volatility model yields lower variance for a minimum variance hedge portfolio than the Black-Scholes model for most classes of options and the differences in variances are statistically significant. The views expressed here are those of the author and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System.

JEL Classification: G13, C52

working papers series