Implied Distribution as a Function of the Volatility Smile
Bankers Markets and Investors, No. 119 (Jul./Aug. 2012), pp. 31-42 (Accepted, July 2011)
20 Pages Posted: 13 Jan 2011 Last revised: 17 Feb 2013
Date Written: June 17, 2011
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.
Keywords: Option pricing, Risk-neutral distribution, Implied volatility smile
JEL Classification: C14, C52, G13
Suggested Citation: Suggested Citation