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

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