2011/01/17 by Gilles Pagès, Pagès, Gilles, Benedikt Wilbertz +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Mathematical Approximation and Integration #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.PR #q-fin.CP #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1101.3228
arxiv created 2011/01/17 · openalex publication_date 2011/01/17 · arxiv updated 2011/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.