Many-core architectures boost the pricing of basket options on adaptive sparse grids
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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Many-core architectures boost the pricing of basket options on adaptive sparse grids. / Heinecke, Alexander; Jepsen, Jacob; Bungartz, Hans Joachim.
WHPCF '13: Proceedings of the 6th Workshop on High Performance Computational Finance. Association for Computing Machinery, 2013. 1.Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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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
Y2 - 18 November 2013 through 18 November 2013
ER -
ID: 169435006