Walter Farkas

## Option Pricing under Lévy Copulas

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.