Short-time asymptotics for marginal distributions of semimartingales
Probability
2012-02-08 v1 Pricing of Securities
Abstract
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.
Keywords
Cite
@article{arxiv.1202.1302,
title = {Short-time asymptotics for marginal distributions of semimartingales},
author = {Amel Bentata and Rama Cont},
journal= {arXiv preprint arXiv:1202.1302},
year = {2012}
}