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Option Pricing for Log-Symmetric Distributions of Returns

Author

Listed:
  • Fima C. Klebaner

    (Monash University)

  • Zinoviy Landsman

    (University of Haifa)

Abstract

We derive an option pricing formula on assets with returns distributed according to a log-symmetric distribution. Our approach is consistent with the no-arbitrage option pricing theory: we propose the natural risk-neutral measure that keeps the distribution of returns in the same log-symmetric family reflecting thus the specificity of the stock’s returns. Our approach also provides insights into the Black–Scholes formula and shows that the symmetry is the key property: if distribution of returns X is log-symmetric then 1/X is also log-symmetric from the same family. The proposed options pricing formula can be seen as a generalization of the Black–Scholes formula valid for lognormal returns. We treat an important case of log returns being a mixture of symmetric distributions with the particular case of mixtures of normals and show that options on such assets are underpriced by the Black–Scholes formula. For the log-mixture of normal distributions comparisons with the classical formula are given.

Suggested Citation

  • Fima C. Klebaner & Zinoviy Landsman, 2009. "Option Pricing for Log-Symmetric Distributions of Returns," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 339-357, September.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:3:d:10.1007_s11009-007-9038-2
    DOI: 10.1007/s11009-007-9038-2
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    References listed on IDEAS

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    Cited by:

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