Option pricing and hedging performance under stochastic volatility and stochastic interest rates

Abstract

Recent studies have extended the Black–Scholes model to incorporate either stochastic interest rates or stochastic volatility. But, there is not yet any comprehensive empirical study demonstrating whether and by how much each generalized feature will improve option pricing and hedging performance. This chapter fills this gap by first developing an implementable option model in closed form that admits both stochastic volatility and stochastic interest rates and that is parsimonious in the number of parameters. The model includes many known ones as special cases. Based on the model, both delta–neutral and singleinstrument minimum–variance hedging strategies are derived analytically. Using S&P 500 option prices, we then compare the pricing and hedging performance of this model with that of three existing ones that respectively allow for (i) constant volatility and constant interest rates (the Black–Scholes), (ii) constant volatility but stochastic interest rates, and (iii) stochastic volatility but constant interest rates. Overall, incorporating stochastic volatility and stochastic interest rates produces the best performance in pricing and hedging, with the remaining pricing and hedging errors no longer systematically related to contract features. The second performer in the horse race is the stochastic volatility model, followed by the stochastic interest rate model and then by the Black–Scholes.