Title: Pricing stock options with stochastic interest rate

Authors: Menachem Abudy; Yehuda Izhakian

Addresses: Graduate School of Business Administration, Bar-Ilan University, Ramat-Gan 52900, Israel ' Department of Finance, Faculty of Management, Tel-Aviv University, Tel-Aviv 69978, Israel

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.

Keywords: pricing stock options; stochastic interest rates; call option; put option; term structure; Black and Scholes model; put-call parity; uncertainty; option prices; modelling; time to maturity; around-the-money options.

DOI: 10.1504/IJPAM.2013.054408

International Journal of Portfolio Analysis and Management, 2013 Vol.1 No.3, pp.250 - 277

Available online: 06 Jun 2013 *

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