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


  • Gilles Pag`es


  • Benedikt Wilbertz



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

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    References listed on IDEAS

    1. Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
    2. Daniel Sevcovic, 2008. "Transformation methods for evaluating approximations to the optimal exercise boundary for linear and nonlinear Black-Scholes equations," Papers 0805.0611,
    3. Tomas Bokes & Daniel Sevcovic, 2009. "Early exercise boundary for American type of floating strike Asian option and its numerical approximation," Papers 0912.1321,
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    Cited by:

    1. 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.

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