Black-Scholes option pricing within Ito and Stratonovich conventions

Options are financial instruments designed to protect investors from the st ock market randomness. In 1973, Black, Scholes and Merton proposed a very p opular option pricing method using stochastic differential equations within the Ito interpretation. Herein, we derive the Black-Scholes equation for t he option price using the Stratonovich calculus along with a comprehensive review, aimed to physicists, of the classical option pricing method based o n the Ito calculus. We show, as can be expected, that the Black-Scholes equ ation is independent of the interpretation chosen. We nonetheless point out the many subtleties underlying Black-Scholes option pricing method. (C) 20 00 Elsevier Science B.V. All rights reserved.