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A Note on the Equivalence between the Normal and the Lognormal Implied Volatility: A Model Free Approach

11 Pages Posted: 25 Jul 2011 Last revised: 29 Nov 2011

Cyril Grunspan

Ecole Superieure d'Ingenierie Leonard de Vinci (ESILV)

Date Written: July 25, 2011

Abstract

First, we show that implied normal volatility is intimately linked with the incomplete Gamma function. Then, we deduce an expansion on implied normal volatility in terms of the time - value of a European call option. Then, we formulate an equivalence between the implied normal volatility and the lognormal implied volatility with any strike and any model. This generalizes a known result for the SABR model. Finally, we address the issue of the 'breakeven move' of a delta - hedged portfolio.

Keywords: smile asymptotics, implied normal volatility, breakeven move

JEL Classification: G12, G13, C65

Suggested Citation

Grunspan, Cyril, A Note on the Equivalence between the Normal and the Lognormal Implied Volatility: A Model Free Approach (July 25, 2011). Available at SSRN: https://ssrn.com/abstract=1894652 or http://dx.doi.org/10.2139/ssrn.1894652

Cyril Grunspan (Contact Author)

Ecole Superieure d'Ingenierie Leonard de Vinci (ESILV) ( email )

92916 Paris La Defense Cedex
France

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