Implied Distribution as a Function of the Volatility Smile | Tavin, Bertrand (1983-....)
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Implied Distribution as a Function of the Volatility Smile

in Bankers, Markets and Investors, 119

ISSN : 1167-4946

Tavin, Bertrand (1983-....)

Voir la revue «Bankers, Markets and Investors»

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.

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