Smile Asymptotics II: Models with Known Moment Generating Function

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dc.creatorBenaim, Shalom
dc.creatorFriz, Peter
dc.date2006-08-24
dc.date.accessioned2026-07-07T07:22:09Z
dc.date.available2026-07-07T07:22:09Z
dc.descriptionIn a recent article the authors obtained a formula which relates explicitly the tail of risk neutral returns with the wing behavior of the Black Scholes implied volatility smile. In situations where precise tail asymptotics are unknown but a moment generating function is available we first establish, under easy-to-check conditions, tail asymptoics on logarithmic scale as soft applications of standard Tauberian theorems. Such asymptotics are enough to make the tail-wing formula work and we so obtain a version of Lee's moment formula with the novel guarantee that there is indeed a limiting slope when plotting implied variance against log-strike. We apply these results to time-changed Levy models and the Heston model. In particular, the term-structure of the wings can be analytically understood.
dc.identifierhttps://arxiv.org/abs/math/0608619
dc.identifierhttp://arxiv.org/abs/math/0608619
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115554
dc.subjectProbability
dc.subject60E99; 91B70
dc.titleSmile Asymptotics II: Models with Known Moment Generating Function
dc.typetext

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