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

TY - GEN

T1 - Many-core architectures boost the pricing of basket options on adaptive sparse grids

AU - Heinecke, Alexander

AU - Jepsen, Jacob

AU - Bungartz, Hans Joachim

N1 - Conference code: 6

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - accelerators

KW - adaptivity

KW - Black-Scholes

KW - finite elements

KW - GPGPU

KW - many-core

KW - SIMD

KW - sparse grids

U2 - 10.1145/2535557.2535560

DO - 10.1145/2535557.2535560

M3 - Article in proceedings

AN - SCOPUS:84891536601

SN - 978-1-4503-2507-3

BT - WHPCF '13

PB - Association for Computing Machinery

T2 - 6th Workshop on High Performance Computational Finance

Y2 - 18 November 2013 through 18 November 2013

ER -