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Black-Scholes option pricing within Ito and Stratonovich conventions

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Author Info
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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File URL: http://arxiv.org/abs/physics/0001040
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number physics/0001040.

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Date of creation: Jan 2000
Date of revision: Apr 2000
Publication status: Published in Physica A 278 (2000) 1-2, 260-274
Handle: RePEc:arx:papers:physics/0001040

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