71 research outputs found
Short-time asymptotics for marginal distributions of semimartingales
We study the short-time asymptotics of conditional expectations of smooth and
non-smooth functions of a (discontinuous) Ito semimartingale; we compute the
leading term in the asymptotics in terms of the local characteristics of the
semimartingale. We derive in particular the asymptotic behavior of call options
with short maturity in a semimartingale model: whereas the behavior of
\textit{out-of-the-money} options is found to be linear in time, the short time
asymptotics of \textit{at-the-money} options is shown to depend on the fine
structure of the semimartingale
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