Ultra-fast scenario analysis of mortgage prepayment risk

Alexios Theiakos, Jurgen Tas, Han van der Lem and Drona Kandhai

Abstract

ABSTRACT

Stochastic scenario analysis of mortgage hedging strategies using single-CPU core machines is often too time consuming. In order to achieve a large practical speedup,we present two methods implemented on a many-core system consisting of graphical processing units (GPUs). The first method is based on Monte Carlo simulations, which are widely used in risk management. The second method relies on a parallel implicit finite difference (FD) discretization of a forward Kolmogorov equation. To estimate the speedup that can be achieved in practice, we compared the performance of both methods with an existing serial trinomial tree implementation on a single CPU core currently in use in our department. For both methods, a large speedup of roughly two orders of magnitude is achieved for realistic workloads.We show that the FD method is approximately four times faster than the Monte Carlo method when implemented on GPUs. On the other hand we argue that the Monte Carlo method is more adaptable to accommodate generic models, while the FD method is typically suitable to lowdimensional models, such as single-factor interest rate models. To our knowledge, the application of GPUs for mortgage hedge calculations is new, as is the implementation of the FD method on GPUs.