Abstract
We prove a small-time Tauberian theorem for transition probabilities of certain Lévy processes. The main assumption is a condition on the asymptotic behavior of the characteristic function. This gives an alternative derivation of some results on digital options and implied volatility slopes in Lévy models. In probabilistic terms, it gives a sufficient criterion for Spitzer’s condition.
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*I gratefully acknowledge the financial support from the Austrian Science Fund (FWF) under grant P 24880-N25.
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Gerhold, S. Small-Maturity Digital Options in Lévy Models: An Analytic Approach* . Lith Math J 55, 222–230 (2015). https://doi.org/10.1007/s10986-015-9275-y
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DOI: https://doi.org/10.1007/s10986-015-9275-y