Cyril Grunspan. A Note on the Equivalence between the Normal and the Lognormal Implied Volatility: A Model Free Approach
Social Sciences / Economics / Financial
Submitted on: Jul 12, 2012, 12:14:48
Description: 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 adress the issue of the "breakeven move" of a delta-hedged portfolio.