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

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

2002-04-15

arxiv.org/abs/cond-mat/0204331v7

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

Physics

Condensed Matter

Statistical Mechanics

final version (published)

Scientific paper

10.1103/PhysRevLett.89.098701

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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