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REGULAR VARIATION AND SMILE ASYMPTOTICS
Author(s) -
Benaim S.,
Friz P.
Publication year - 2009
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2008.00354.x
Subject(s) - sharpening , mathematics , variation (astronomy) , simple (philosophy) , moment (physics) , volatility (finance) , mathematical economics , econometrics , statistical physics , calculus (dental) , computer science , classical mechanics , physics , philosophy , epistemology , medicine , dentistry , astrophysics , computer vision
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.