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Market Implied Probability Distributions and Bayesian Skew Estimation

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  • Ulrich Kirchner
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    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.

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    File URL: http://arxiv.org/pdf/0911.0805
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0911.0805.

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    Date of creation: Nov 2009
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    Handle: RePEc:arx:papers:0911.0805

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    Web page: http://arxiv.org/

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    Cited by:
    1. Ulrich Kirchner, 2010. "A Subjective and Probabilistic Approach to Derivatives," Papers 1001.1616, arXiv.org.
    2. 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, Springer, vol. 79(1), pages 47-53, January.
    3. Ulrich Kirchner, 2010. "Managing Derivative Exposure," Papers 1004.1053, arXiv.org.

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