research-article

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

Authors:

Alexander Heinecke,

Hans-Joachim BungartzAuthors Info & Claims

WHPCF '13: Proceedings of the 6th Workshop on High Performance Computational Finance

Article No.: 1, Pages 1 - 9

https://doi.org/10.1145/2535557.2535560

Published: 18 November 2013 Publication History

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.

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Cited By

Scheidegger STreccani A(2018)Pricing American Options under High-Dimensional Models with Recursive Adaptive Sparse Expectations*Journal of Financial Econometrics10.1093/jjfinec/nby024Online publication date: 31-Oct-2018
https://doi.org/10.1093/jjfinec/nby024
Moca MMoldovan DLodygensky OFedak G(2016)E-Fast & CloudPower: Towards High Performance Technical Analysis for Small InvestorsEconomics of Grids, Clouds, Systems, and Services10.1007/978-3-319-43177-2_16(236-248)Online publication date: 20-Jul-2016
https://doi.org/10.1007/978-3-319-43177-2_16
Scheidegger STreccani A(undefined)Pricing American Options Under High-Dimensional Models with Recursive Adaptive Sparse ExpectationsSSRN Electronic Journal10.2139/ssrn.2867926
https://doi.org/10.2139/ssrn.2867926

Index Terms

Many-core architectures boost the pricing of basket options on adaptive sparse grids
1. Mathematics of computing
  1. Mathematical software

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cover image ACM Conferences

WHPCF '13: Proceedings of the 6th Workshop on High Performance Computational Finance

November 2013

65 pages

ISBN:9781450325073

DOI:10.1145/2535557

Copyright © 2013 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Publication History

Published: 18 November 2013

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Gauss Centre for Supercomputing

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SC13

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SC13: International Conference for High Performance Computing, Networking, Storage and Analysis

November 18, 2013

Colorado, Denver

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Cited By

Scheidegger STreccani A(2018)Pricing American Options under High-Dimensional Models with Recursive Adaptive Sparse Expectations*Journal of Financial Econometrics10.1093/jjfinec/nby024Online publication date: 31-Oct-2018
https://doi.org/10.1093/jjfinec/nby024
Moca MMoldovan DLodygensky OFedak G(2016)E-Fast & CloudPower: Towards High Performance Technical Analysis for Small InvestorsEconomics of Grids, Clouds, Systems, and Services10.1007/978-3-319-43177-2_16(236-248)Online publication date: 20-Jul-2016
https://doi.org/10.1007/978-3-319-43177-2_16
Scheidegger STreccani A(undefined)Pricing American Options Under High-Dimensional Models with Recursive Adaptive Sparse ExpectationsSSRN Electronic Journal10.2139/ssrn.2867926
https://doi.org/10.2139/ssrn.2867926

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