Bertram Düring
Department of Mathematics, University of Sussex, UK
We consider a class of parabolic partial differential equations with time and space dependent coefficients as well as with mixed second-order derivative terms. Problems of this type arise frequently in computational finance. We follow a high-order compact finite difference approach and derive general conditions on the coefficients which allow us to obtain a high-order compact scheme which is fourth-order accurate in space and second-order accurate in time.
We discuss the Neumann stability analysis of the Cauchy problem in two and three spatial dimensions for vanishing mixed derivative terms, and also give partial results for the general case. The results suggest unconditional stability of the scheme. We present numerical results for pricing of options in a number of popular option pricing models