Gyongy has shown that it is possible to construct a diffusion process with the same one-dimensional marginal distributions as a given initial Ito process. This is closely related to work by Dupire that shows how to construct a local volatility model such that the European option prices implied by the model agree with a given set of market prices. In this talk, we review this connection and then provide a generalization of Gyongy's Theorem that shows how one can match more properties of an initial Ito process by carrying more information about the path history in the mimicking Markov process. Finally, we suggest how such a construction might allow one to extend the local volatility methodology and construct price processes which fit the market prices of mildly path-dependent options. ( Slides)
Speaker: Gerard Brunick, Carnegie Mellon University