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

摘要

First, we show that implied normal volatility is intimately linked with theincomplete Gamma function. Then, we deduce an expansion on implied normalvolatility in terms of the time-value of a European call option. Then, weformulate an equivalence between the implied normal volatility and thelognormal implied volatility with any strike and any model. This generalizes aknown result for the SABR model. Finally, we adress the issue of the "breakevenmove" of a delta-hedged portfolio.