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Implied Distribution as a Function of the Volatility Smile

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  • Bertrand Tavin

    (EM - EMLyon Business School)

Abstract

The aim of this paper is to obtain the risk-neutral density of an underlying asset price as a function of its option implied volatility smile. We derive a known closed form non-parametric expression for the density and decompose it into a sum of lognormal and adjustment terms. By analyzing this decomposition we also derive two no-arbitrage conditions on the volatility smile. We then explain how to use the results. Our methodology is applied first to the pricing of a portfolio of digital options in a fully smile-consistent way. It is then applied to the fitting of a parametric distribution for log-return modelling, the Normal Inverse Gaussian.

Suggested Citation

  • Bertrand Tavin, 2012. "Implied Distribution as a Function of the Volatility Smile," Post-Print hal-02313144, HAL.
    • Handle: RePEc:hal:journl:hal-02313144
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