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The Edgeworth And Gram–Charlier Densities

Author

Listed:
  • PAKORN ASCHAKULPORN

    (Department of Accountancy and Finance, University of Otago, Otago Business School, Dunedin 9016, New Zealand)

  • JIN E. ZHANG

    (Department of Accountancy and Finance, University of Otago, Otago Business School, Dunedin 9016, New Zealand)

Abstract

This paper is the first to define the Edgeworth density and comprehensively compare it to the Gram–Charlier density in the context of option pricing. The two densities allow additional cumulants to the normal distribution; although similar, they are not the same when truncated. Many academics have misidentified the two. This paper clearly distinguishes the two, presents the derivation of both, and develops a general option pricing model which can be used for both densities with an arbitrary number of additional cumulants. The option pricing formula for each density is also calibrated and compared to more typical models with the most advanced being the affine jump-diffusion model (stochastic volatility with double jumps).

Suggested Citation

  • Pakorn Aschakulporn & Jin E. Zhang, 2024. "The Edgeworth And Gram–Charlier Densities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 27(05n06), pages 1-50, September.
    • Handle: RePEc:wsi:ijtafx:v:27:y:2024:i:05n06:n:s0219024924500201
    DOI: 10.1142/S0219024924500201
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