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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)

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    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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    File URL: http://arxiv.org/pdf/1101.3228
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1101.3228.

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    Date of creation: Jan 2011
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    Handle: RePEc:arx:papers:1101.3228

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    Web page: http://arxiv.org/

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