We begin by discussing the challenges surrounding the solution of high-dimensional PDE models in finance. Sparse grids are shown to give optimal complexity among grid-based methods and we discuss their limitations on the example of equity and credit baskets. Alternatively, an asymptotic expansion of the value function around the principal component of the driving diffusion process is derived and proves to give very accurate results for index options. Finally, we present a unifying framework for these two concepts and discuss alternative approaches using stochastic partial differential equations as models for large (credit) baskets.

At Oxford, Dr Christoph Reisinger is a member of the Mathematical and Computational Finance Group, the Academic Director of the Mathematical Finance programme, Tutorial Fellow and Senior Maths Tutor at St Catherine's College, and an Associate Member of Oxford-Man Institute of Quantitative Finance. He is in Sydney on a visit to CSIRO.