Pricing stock options with stochastic interest rate

Abstract

This paper constructs a closed-form generalization of the Black-Scholes model for the case where the short-term interest rate follows a stochastic Gaussian process. Capturing this additional source of uncertainty appears to have a considerable effect on option prices. We show that the value of the stock option increases with the volatility of the interest rate and with time to maturity. Our empirical tests support the theoretical model and demonstrate a significant pricing improvement relative to the Black-Scholes model. The magnitude of the improvement is a positive function of the option's time to maturity, the largest improvement being obtained for around-the-money options.