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GPGPUs in computational finance: Massive parallel computing for American style options

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  • Gilles Pag`es

    (PMA)

  • Benedikt Wilbertz

    (PMA)

Abstract

The pricing of American style and multiple exercise options is a very challenging problem in mathematical finance. One usually employs a Least-Square Monte Carlo approach (Longstaff-Schwartz method) for the evaluation of conditional expectations which arise in the Backward Dynamic Programming principle for such optimal stopping or stochastic control problems in a Markovian framework. Unfortunately, these Least-Square Monte Carlo approaches are rather slow and allow, due to the dependency structure in the Backward Dynamic Programming principle, no parallel implementation; whether on the Monte Carlo levelnor on the time layer level of this problem. We therefore present in this paper a quantization method for the computation of the conditional expectations, that allows a straightforward parallelization on the Monte Carlo level. Moreover, we are able to develop for AR(1)-processes a further parallelization in the time domain, which makes use of faster memory structures and therefore maximizes parallel execution. Finally, we present numerical results for a CUDA implementation of this methods. It will turn out that such an implementation leads to an impressive speed-up compared to a serial CPU implementation.

Suggested Citation

  • Gilles Pag`es & Benedikt Wilbertz, 2011. "GPGPUs in computational finance: Massive parallel computing for American style options," Papers 1101.3228, arXiv.org.
    • Handle: RePEc:arx:papers:1101.3228
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Pierre L'Ecuyer & Richard Simard & E. Jack Chen & W. David Kelton, 2002. "An Object-Oriented Random-Number Package with Many Long Streams and Substreams," Operations Research, INFORMS, vol. 50(6), pages 1073-1075, December.
    3. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    4. Anne Laure Bronstein & Gilles Pages & Benedikt Wilbertz, 2010. "How to speed up the quantization tree algorithm with an application to swing options," Quantitative Finance, Taylor & Francis Journals, vol. 10(9), pages 995-1007.
    5. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168, January.
    6. Olivier Bardou & Sandrine Bouthemy & Gilles Pages, 2009. "Optimal Quantization for the Pricing of Swing Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(2), pages 183-217.
    7. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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    Cited by:

    1. Bonollo, Michele & Di Persio, Luca & Oliva, Immacolata, 2020. "A quantization approach to the counterparty credit exposure estimation," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 335-356.
    2. Michele Bonollo & Luca Di Persio & Luca Mammi & Immacolata Oliva, 2017. "Estimating the Counterparty Risk Exposure by using the Brownian Motion Local Time," Papers 1704.03244, arXiv.org.
    3. I. Róbert Sipos & Attila Ceffer & János Levendovszky, 2017. "Parallel Optimization of Sparse Portfolios with AR-HMMs," Computational Economics, Springer;Society for Computational Economics, vol. 49(4), pages 563-578, April.
    4. Jérôme Lelong, 2020. "Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach," Post-Print hal-01983115, HAL.
    5. Céline Labart & Jérôme Lelong, 2011. "A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options," Working Papers hal-00567729, HAL.

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