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

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

2011-12-08

arxiv.org/abs/1112.1782v1

Economy

Quantitative Finance

Pricing of Securities

10 pages

Scientific paper

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.

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