Implied Distribution as a Function of the Volatility Smile

Bertrand Tavin
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Bertrand Tavin: EM - EMLyon Business School

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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.

Date: 2012-07-01
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Published in Bankers Markets & Investors : an academic & professional review, 2012, 119, pp.31-42 P

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02313144

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