Pricing Stock Options with Stochastic Interest Rate

Abstract:     
This paper constructs a closed-form generalization of the Black-Scholesmodel for the case where the short-term interest rate follows astochastic Gaussian process. Capturing this additional source ofuncertainty appears to have a considerable effect on option prices. Weshow that the value of the stock option increases with the volatility ofthe interest rate and with time to maturity. Our empirical tests supportthe theoretical model and demonstrate a significant pricing improvementrelative to the Black-Scholes model. The magnitude of the improvement isa positive function of the option's time to maturity, the largestimprovement being obtained for around-the-money options.

Number of Pages in PDF File: 46

Keywords: Option, call option, put option, stochastic interest rate, term structure of interest rates, Black and Scholes, put-call parity

working papers series