Pricing stock options with stochastic interest rate

Abstract

This paper constructs a closed-form generalisation 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 a stock option increases with the volatility of the interest rate and with its time to maturity. The 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.