On the use of the Black & Scholes model in a stochastic interest rate economy

This paper examines the pelformance of the Black & Scholes (1973) model for pricing of European style stock options in a stochastic interest rate economy. Throughout the paper we assume that Jarrow"s (1988) version of the Merton (1973) model correctly describes the reality. We examine the implications of two standard estimation methods of the value of the volatility parameter in the Black & Scholes model, the historical estimate method and the implied value method, respectively. Specific formulae are given in order to determine 'whether the Black & Scholes model under- or overprices options. Numerical examples show that, in some cases, the pricing error can be sizeable even for short term options.