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

Bertrand Tavin

EMLYON Business School

Date Written: June 17, 2011

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.

Keywords: Option pricing, Risk-neutral distribution, Implied volatility smile

JEL Classification: C14, C52, G13

Suggested Citation

Tavin, Bertrand, Implied Distribution as a Function of the Volatility Smile (June 17, 2011). Bankers Markets and Investors, No. 119 (Jul./Aug. 2012), pp. 31-42 (Accepted, July 2011). Available at SSRN: https://ssrn.com/abstract=1738965 or http://dx.doi.org/10.2139/ssrn.1738965

Bertrand Tavin (Contact Author)

EMLYON Business School ( email )

23 Avenue Guy de Collongue
Ecully, 69132
France

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