A Note on the Equivalence between the Normal and the Lognormal Implied Volatility: A Model Free Approach
Ecole Superieure d'Ingenierie Leonard de Vinci (ESILV)
July 25, 2011
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
Date posted: July 25, 2011 ; Last revised: November 29, 2011