Regular Variation and Smile Asymptotics

2006/03/06 by Shalom Benaim, Benaim, Shalom, Peter Friz +1 · 2 citations
Mathematics · #60E99 #91B70 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60E99 #msc:91B70

paper · pdf · doi:10.48550/arxiv.math/0603146

arxiv created 2006/03/07 · arxiv updated 2009/12/01

Abstract

We consider risk-neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated moment formula. The theory of regular variation provides the ideal mathematical framework to formulate and prove such results. The practical value of our formulae comes from the vast literature on tail asymptotics and our conditions are often seen to be true by simple inspection of known results.

Cited by

• Smile asymptotics for Bachelier implied volatility
• Arbitrage-Free Multi-Maturity Risk-Neutral Marginals

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