PreprintImplied volatility: small timetoexpiry asymptotics in exponential Lévy modelsMichael RoperAbstractIn this paper, we examine the small timetoexpiry behaviour of implied volatility in models of exponential Lévy type. In the atthemoney case, it turns out that the implied volatility converges, as timetoexpiry goes to zero, to the square root of the Gaussian member of the driving Lévy process’ characteristic triplet. In particular, the limit is zero if the Lévy process has no Gaussian part. In the not atthemoney case, there are a number of possible behaviours. In most cases of interest, however, the implied volatility goes to infinity as timetoexpiry goes to zero. It is also shown that there are exponential Lévy models in which the implied volatility converges to zero as timetoexpiry goes to zero. Keywords: Implied volatility; Levy processes.
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