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

Grunspan, Cyril

doi:10.2139/ssrn.1894652

Abstract

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

Cyril Grunspan

Ecole Superieure d'Ingenierie Leonard de Vinci (ESILV)

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.

Number of Pages in PDF File: 11

Keywords: smile asymptotics, implied normal volatility, breakeven move

JEL Classification: G12, G13, C65

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Date posted: July 25, 2011 ; Last revised: November 29, 2011

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: http://ssrn.com/abstract=1894652 or http://dx.doi.org/10.2139/ssrn.1894652

Contact Information

Cyril Grunspan (Contact Author)

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

92916 Paris La Defense Cedex
France