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

Lisa Borland

Papers from arXiv.org

Abstract: Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter $q$. A generalized form of the Black-Scholes (B-S) partial differential equation, and some closed-form solutions are obtained. The standard B-S equation ($q=1$) which is used by economists to calculate option prices requires multiple values of the stock volatility (known as the volatility smile). Using $q=1.5$ which well models the empirical distribution of returns, we get a good description of option prices using a single volatility.

Date: 2002-04, Revised 2002-09
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Citations: View citations in EconPapers (29)

Published in Phys. Rev. Lett. 89, N9, 098701, August 2002

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