Pricing and hedging index options under stochastic volatility: an empirical examination

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.