A finite volume approach for contingent claims valuation

This paper presents a finite volume approach for solving two-dimensionalcontingent claims valuation problems. The contingent claimsPDEs are in non-divergence form. The finite volume method ismore flexible than finite difference schemes which are oftendescribed in the finance literature and frequently used in practice.Moreover, the finite volume method naturally handles cases wherethe underlying partial differential equation becomes convectiondominated or degenerate. A compact method is developed whichuses a high-order flux limiter for the convection terms. Thispaper will demonstrate how a variety of two-dimensional valuationproblems can all be solved using the same approach. The generalityof the approach is in part due to the fact that changes causedby different model specifications are localized. Constraintson the solution are treated in a uniform manner using a penaltymethod. A variety of illustrative example computations are presented.