2000/01/31 by J Perelló, J. Perello, J.M Porrà +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Mathematical Approximation and Integration #Stochastic processes and financial applications #cond-mat.stat-mech #physics.data-an #physics.soc-ph #q-fin.PR
paper · pdf · doi:10.1016/s0378-4371(99)00612-3
published as Physica A 278 (2000) 1-2, 260-274 · 14 pages
openalex publication_date 2000/04/01 · arxiv created 2000/04/07 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.