A finite volume approach for contingent claims valuation

This paper presents a finite volume approach for solving two-dimensional co ntingent claims valuation problems. The contingent claims PDEs are in non-d ivergence form. The finite volume method is more flexible than finite diffe rence schemes which are often described in the finance literature and frequ ently used in practice. Moreover, the finite volume method naturally handle s cases where the underlying partial differential equation becomes convecti on dominated or degenerate. A compact method is developed which uses a high -order flux limiter for the convection terms. This paper will demonstrate h ow a variety of two-dimensional valuation problems can all be solved using the same approach. The generality of the approach is in part due to the fac t that changes caused by different model specifications are localized. Cons traints on the solution are treated in a uniform manner using a penalty met hod, A variety of illustrative example computations are presented.