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
Date Written: 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.
Keywords: smile asymptotics, implied normal volatility, breakeven move
JEL Classification: G12, G13, C65
Suggested Citation: Suggested Citation