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Black-Scholes option pricing within Itô and Stratonovich conventions
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Options are 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 Itô 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 Itô 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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PERELLÓ, Josep, et al. Black-Scholes option pricing within Itô and Stratonovich conventions. Physica A. 2000. Vol. 278, num. 1-2, pags. 260-274. ISSN 0378-4371. [consulted: 3 of August of 2026]. Available at: https://hdl.handle.net/2445/119285