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Black-Scholes option pricing within Ito and Stratonovich conventions

J. Perello·J. M. Porra·M. Montero·J. Masoliver
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Abstract

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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J. Perello, J. M. Porra, M. Montero, J. Masoliver. 2000-04-07. Black-Scholes option pricing within Ito and Stratonovich conventions. https://doi.org/10.1016/s0378-4371(99)00612-3

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