Black-Scholes option pricing within Ito and Stratonovich conventions

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.

14 pages

References in corpus (1)

• Price Variations in a Stock Market With Many Agents

Cited by in corpus (7)

• Stochastic volatility and leverage effect
• A correlated stochastic volatility model measuring leverage and other stylized facts
• Black-Scholes model under subordination
• The effect of non-ideal market conditions on option pricing
• Option pricing and perfect hedging on correlated stocks
• Combined Mutiplicative-Heston Model for Stochastic Volatility
• Distributions of Historic Market Data - Stock Returns