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

2011/12/08 by Cyril Grunspan, Grunspan, Cyril
Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #Financial Markets and Investment Strategies #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications #q-fin.PR

paper · pdf · doi:10.48550/arxiv.1112.1782

10 pages

arxiv created 2011/12/08 · openalex publication_date 2011/12/08 · arxiv updated 2011/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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