Closed Form Option Pricing Formulas based on a non-Gaussian Stock Price Model

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  • 19 June 2002
Abstract
A closed form option pricing formula is obtained, based on a stochastic model with statistical feedback. The fluctuations evolve according to a Tsallis distribution which fits empirical data for stock returns. A generalized form of the Black-Scholes PDE is derived, parametrized by the Tsallis entropic index q. A martingale representation is found, which allows us to use concepts of risk-free asset pricing theory. We explicitly solve the case of European options and the exact solutions which are found capture features of real option prices, such as the volatility smile.

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