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Option pricing for non-Gaussian price fluctuations

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  • Kleinert, Hagen

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.

Suggested Citation

  • Kleinert, Hagen, 2004. "Option pricing for non-Gaussian price fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 151-159.
    • Handle: RePEc:eee:phsmap:v:338:y:2004:i:1:p:151-159
    DOI: 10.1016/j.physa.2004.02.037
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    References listed on IDEAS

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    1. Neil Shephard & Ole E. Barndorff-Nielsen, 2000. "Modelling by Levy Processes for Financial Econometrics," Economics Series Working Papers 2000-W03, University of Oxford, Department of Economics.
    2. Neil Shephard & Ole E. Barndorff-Nielsen, 1998. "Incorporation of a Leverage Effect in a Stochastic Volatility Model," Economics Series Working Papers 1998-W14, University of Oxford, Department of Economics.
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    Cited by:

    1. Capuozzo, Pietro & Panella, Emanuele & Schettini Gherardini, Tancredi & Vvedensky, Dimitri D., 2021. "Path integral Monte Carlo method for option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    2. Paolinelli, Giovanni & Arioli, Gianni, 2019. "A model for stocks dynamics based on a non-Gaussian path integral," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 499-514.
    3. Giovanni Paolinelli & Gianni Arioli, 2018. "A model for stocks dynamics based on a non-Gaussian path integral," Papers 1809.01342, arXiv.org, revised Oct 2018.

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    Keywords

    Non-Gaussian fluctuations; Option pricing;

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