Option Pricing and Hedging Performance Under Stochastic Volatility and Stochastic Interest Rates

Recent studies have extended the Black–ScholesBlack-Scholes model model to incorporate either stochastic interest rates or stochastic volatility. However, there is not yet any comprehensive empirical study demonstrating whether and by how much each generalized feature will improve option pricingOption pricing and hedging performanceHedging 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. Both delta-neutral and single-instrument minimum-variance hedgingHedging strategies are derived analytically. Using S&P 500 option prices, we then compare the pricing and hedging performanceHedging 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 hedgingHedging, with the remaining pricing and hedgingHedging 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 rates model and then by the Black–Scholes.