SMILE ASYMPTOTICS II: MODELS WITH KNOWN MOMENT GENERATING FUNCTIONS

By Shalom Benaim, Peter K. Friz. 2006

73 citations recorded by the source corpus.

The tail of risk neutral returns can be related explicitly with the wing behaviour of the Black-Scholes implied volatility smile. In situations where precise tail asymptotics are unknown but a moment generating function is available we establish, under easy-to-check Tauberian conditions, tail asymptotics on logarithmic scales. Such asymptotics are enough to make the tail-wing formula (see Benaim and Friz (2008)) work and so we obtain, under generic conditions, a limiting slope when plotting the square of the implied volatility against the log strike, improving a lim sup statement obtained earlier by Lee (2004). We apply these results to time-changed exponential Levy models and examine several popular models in more detail, both analytically and numerically.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3114b0b87b7847a309857aae0f48dce7379c9f1d

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Citations in the corpus

Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results (2012, background): “follow from the moment formulas of [69], [15], [16] and [55]; see [116] for a brief discussion.”
Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations (2011, background): “We note that the square-root growth of implied volatility, in terms of log-strike, is actually a very general feature of models with moment explosions, [38, 7] which includes many stochastic volatility models [24, 39, 8].”