Anisotropic Stable Levy Copula Processes - Analytical and Numerical Aspects

We consider the valuation of derivative contracts on baskets where prices of single assets are Levy-like Feller processes of tempered stable type. The dependence among the marginals' jump structure is parametrized by a Levy copula. For marginals of regular, exponential Levy type in the sense of Boyarchenko and Levendorskii we show that the infinitesimal generator ${\cal A}$ of the resulting Levy copula process is a pseudo-differential operator whose principal symbol is a distribution of anisotropic homogeneity.We analyze the jump measure of the corresponding Levy copula processes. We prove the domains of their infinitesimal generators ${\cal A}$ are certain anisotropic Sobolev spaces. In these spaces and for a large class of Levy copulas, we prove a Garding inequality for ${\cal A}$.We design a wavelet-based dimension-independent tensor product discretization for the efficient numerical solution of the parabolic Kolmogoroff equation $u_t {\cal A}u = 0$ arising in valuation of derivative contracts under possibly stopped Levy copula processes. We show that diagonal preconditioning yields bounded condition number of the resulting matrices