Black-Scholes option pricing within Ito and Stratonovich conventions

Details Black-Scholes option pricing within Ito and Stratonovich conventions Black-Scholes option pricing within Ito and Stratonovich conventions

2000-01-19

arxiv.org/abs/physics/0001040v2

Physica A 278 (2000) 1-2, 260-274

Physics

Physics and Society

14 pages

Scientific paper

10.1016/S0378-4371(99)00612-3

Options financial instruments designed to protect investors from the stock market randomness. In 1973, Fisher Black, Myron Scholes and Robert Merton proposed a very popular option pricing method using stochastic differential equations within the Ito interpretation. Herein, we derive the Black-Scholes equation for the option price using the Stratonovich calculus along with a comprehensive review, aimed to physicists, of the classical option pricing method based on the Ito calculus. We show, as can be expected, that the Black-Scholes equation is independent of the interpretation chosen. We nonetheless point out the many subtleties underlying Black-Scholes option pricing method.

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