Regular Variation and Smile Asymptotics

Details Regular Variation and Smile Asymptotics Regular Variation and Smile Asymptotics

2006-03-06

arxiv.org/abs/math/0603146v2

Mathematics

Probability

Scientific paper

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.

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