Option pricing for non-Gaussian price fluctuations

Hagen Kleinert

Physica A: Statistical Mechanics and its Applications, 2004, vol. 338, issue 1, 151-159

Abstract: From the path integral description of price fluctuations with non-Gaussian distributions we derive a stochastic calculus which replaces Itô's calculus for harmonic fluctuations. We set up a natural martingale for option pricing from the wealth balance of options, stocks, and bonds, and evaluate the resulting formula for truncated Lévy distributions. After this, an alternative formula is derived for a model of multivariant Gaussian price fluctuations which leads to non-Gaussian return distributions fitting Dow Jones data excellently from long to short time scales with a tail behavior e−x/x3/2.

Keywords: Non-Gaussian fluctuations; Option pricing (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:338:y:2004:i:1:p:151-159

DOI: 10.1016/j.physa.2004.02.037

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