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