Many-core architectures boost the pricing of basket options on adaptive sparse grids

Abstract

In this work, we present a highly scalable approach for numerically solving the Black-Scholes PDE in order to price basket options. Our method is based on a spatially adaptive sparse-grid discretization with finite elements. Since we cannot unleash the compute capabilities of modern many-core chips such as GPUs using the complexity-optimal Up-Down method, we implemented an embarrassingly parallel direct method. This operator is paired with a distributed memory parallelization using MPI and we achieved very good scalability results compared to the standard Up-Down approach. Since we exploit all levels of the operator's parallelism, we are able to achieve nearly perfect strong scaling for the Black-Scholes solver. Our results show that typical problem sizes (5 dimensional basket options), require at least 4 NVIDIA K20X Kepler GPUs (inside a Cray XK7) in order to be faster than the Up-Down scheme running on 16 Intel Sandy Bridge cores (one box). On a Cray XK7 machine we outperform our highly parallel Up-Down implementation by 55X with respect to time to solution. Both results emphasize the competitiveness of our proposed operator.