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Market Implied Probability Distributions and Bayesian Skew Estimation

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  • Ulrich Kirchner

Abstract

We review and illustrate how the volatility smile translates into a probability distribution, the market-implied probability distribution representing believes priced in. The effects of changes in the smile are examined. Special attention is given to the effects of slope, which might appear at first counter-intuitive. We then show how Bayesian methods can be used to deal with sparse real market data. With each skew in a parametric model we associate a probability. This is illustrated with an example, for which multivariate parameter distributions are derived. We introduce the fuzzy smile (or fuzzy skew) as a visual illustration of the skew distribution.

Suggested Citation

  • Ulrich Kirchner, 2009. "Market Implied Probability Distributions and Bayesian Skew Estimation," Papers 0911.0805, arXiv.org.
  • Handle: RePEc:arx:papers:0911.0805
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    File URL: http://arxiv.org/pdf/0911.0805
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    Cited by:

    1. Ulrich Kirchner, 2010. "Managing Derivative Exposure," Papers 1004.1053, arXiv.org.
    2. Ulrich Kirchner, 2010. "A Subjective and Probabilistic Approach to Derivatives," Papers 1001.1616, arXiv.org.
    3. L. Spadafora & G. P. Berman & F. Borgonovi, 2011. "Adiabaticity conditions for volatility smile in Black-Scholes pricing model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 79(1), pages 47-53, January.

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