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Gram-Charlier Processes and Applications to Option Pricing

Author

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  • Jean-Pierre Chateau
  • Daniel Dufresne

Abstract

A Gram-Charlier distribution has a density that is a polynomial times a normal density. For option pricing this retains the tractability of the normal distribution while allowing nonzero skewness and excess kurtosis. Properties of the Gram-Charlier distributions are derived, leading to the definition of a process with independent Gram-Charlier increments, as well as formulas for option prices and their sensitivities. A procedure for simulating Gram-Charlier distributions and processes is given. Numerical illustrations show the effect of skewness and kurtosis on option prices.

Suggested Citation

  • Jean-Pierre Chateau & Daniel Dufresne, 2017. "Gram-Charlier Processes and Applications to Option Pricing," Journal of Probability and Statistics, Hindawi, vol. 2017, pages 1-19, February.
    • Handle: RePEc:hin:jnljps:8690491
    DOI: 10.1155/2017/8690491
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    Cited by:

    1. Liexin Cheng & Xue Cheng, 2024. "Decomposing Smiles: A Time Change Approach," Papers 2401.03776, arXiv.org, revised Jan 2024.
    2. Sara Cecchetti & Adriana Grasso & Marcello Pericoli, 2022. "An analysis of objective inflation expectations and inflation risk premia," Temi di discussione (Economic working papers) 1380, Bank of Italy, Economic Research and International Relations Area.

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