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

Gilles Pages, Benedikt Wilbertz
Laboratoire de Probabilites et Mod’eles aleatoires, UMR 7599, Universit?e Paris 6, case
arXiv:1101.3228 [q-fin.CP] (17 Jan 2011)

@article{2011arXiv1101.3228P,

   author={Pag{‘e}s}, G. and {Wilbertz}, B.},

   title={“{GPGPUs in computational finance: Massive parallel computing for American style options}”},

   journal={ArXiv e-prints},

   archivePrefix={“arXiv”},

   eprint={1101.3228},

   primaryClass={“q-fin.CP”},

   keywords={Quantitative Finance – Computational Finance, Mathematics – Probability},

   year={2011},

   month={jan},

   adsurl={http://adsabs.harvard.edu/abs/2011arXiv1101.3228P},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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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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