Walter Farkas

This is a joint work with Christoph Schwab (ETH Zurich). We consider the valuation of derivative contracts on baskets where prices of single assets are Lévy like Feller processes. The dependence among the marginals' jump structure is parametrized by a Lévy copula. For marginals of regular, exponential Lévy type we show that the infinitesimal generator $A$ of the resulting Lévy copula process is a pseudodifferential operator whose principal symbol has mixed homogeneity.
We analyze the jump measure of Lévy copula processes. We prove the domains of the infinitesimal generators $A$ of Lévy copula processes are certain anisotropic Sobolev spaces of mixed homogeneity.
We design a dimension-independent method for the efficient numerical solution of the parabolic Kolmogorov equation $u_t+Au = 0$ arising in valuation of derivative contracts under possibly stopped Lévy copula processes.