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Preposterior analysis for option pricing

Author

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  • Dorje Brody
  • Ian Buckley
  • Bernhard Meister

Abstract

The second partial derivative of a European-style vanilla option with respect to the current price of the underlying asset—the option gamma—defines a probability density function for the current underlying price. By use of entropy maximization it is possible to obtain an option gamma, from which the associated option pricing formula can be recovered by integration. A number of pricing formulae are obtained in this manner, corresponding to different specifications of the constraints. When the available market information consists solely of a set of traded option prices, the entropic formulation leads to a model-independent calibration procedure. The result thus obtained also allows one to recover the relevant Greeks.

Suggested Citation

  • Dorje Brody & Ian Buckley & Bernhard Meister, 2004. "Preposterior analysis for option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 465-477.
  • Handle: RePEc:taf:quantf:v:4:y:2004:i:4:p:465-477
    DOI: 10.1080/14697680400008676
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    Cited by:

    1. C. Neri & L. Schneider, 2012. "The Impact of the Prior Density on a Minimum Relative Entropy Density: A Case Study with SPX Option Data," Papers 1201.2616, arXiv.org, revised Sep 2013.
    2. Cassio Neri & Lorenz Schneider, 2012. "Maximum entropy distributions inferred from option portfolios on an asset," Finance and Stochastics, Springer, vol. 16(2), pages 293-318, April.

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