Pricing Stock Options under Stochastic Volatility and Stochastic Interest Rates with Efficient Method of Moments Estimation

While the stochastic volatility (SV) generalization has been shown to improvethe explanatory power compared to the Black-Scholes model, the empiricalimplications of the SV models on option pricing have not been adequately tested.The purpose of this paper is to first estimate a multivariate SV model using theefficient method of moments (EMM) technique and then investigate the respectiveeffect of stochastic interest rate, systematic volatility and idiosyncraticvolatility on option prices. We compute option prices using both underlyinghistorical volatilities obtained through reprojection and volatilities impliedfrom observed option prices and gauge each model's performance through directcomparison with observed market option prices. Our results suggest: (i) Whiletheory predicts that the short-term interest rates are strongly related to thesystematc volatility of the consumption process, our estimation results suggestthat the short-term interest rate fails to be a good proxy of the systematicfactor; (ii) While allowing for stochastic volatility of stock returns can ingeneral reduce the pricing errors and allowing for asymmetry or "leverageeffect'' in the SV models does help to explain the skewness of the volatility"smile'', allowing for stochastic interest rate has minimal impact on optionprices in our case; (iii) Similar to Melino and Turnbull (1990), our empiricalfindings strongly suggest the existence of a non-zero risk premum for stochasticvolatility of stock returns. Allowing for non-zero risk-premium of stochasticvolatility and based on implied volatility, the SV models can largely reduce theoption pricing errors, suggesting the importance of incorporating theinformation in the options market in pricing options.