Mimicking the marginal distributions of a semimartingale

A. Bentata, Université Pierre et Marie Curie, Paris, France

Monday, October 26
at 15.15, HG E 1.1

We give conditions under which the flow of marginal distributions of a discontinuous semimartingale X can be matched by a Markov process whose infinitesimal generator is expressed in terms of the local characteristics of X. Our results extend previous results of Gyongy (1986) to discontinuous semimartingales. Our results allows to derive a forward partial integro-differential equation for option prices in a large class of (non-Markovian) semimartingale models with jumps. This equation generalizes the classical result of Dupire (1994) to the case of jump processes. We discuss applications to time-changed Levy processes and index options.