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

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.
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Preprints, Working Papers, ...
2011
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https://hal.archives-ouvertes.fr/hal-00556544
Contributor : Benedikt Wilbertz <>
Submitted on : Monday, January 17, 2011 - 11:07:29 AM
Last modification on : Monday, May 29, 2017 - 2:26:42 PM
Document(s) archivé(s) le : Thursday, June 30, 2011 - 1:48:29 PM

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  • HAL Id : hal-00556544, version 1
  • ARXIV : 1101.3228

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Gilles Pagès, Benedikt Wilbertz. GPGPUs in computational finance: Massive parallel computing for American style options. 2011. <hal-00556544>

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