2011/02/23 by Céline Labart, Labart, Céline, Jérôme Lelong +1
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Approximation and Integration #Parallel #Probability (math.PR) #Risk and Portfolio Optimization #Simulation Techniques and Applications #Stochastic processes and financial applications #and Cluster Computing (cs.DC) #cs.DC #math.PR
paper · pdf · doi:10.48550/arxiv.1102.4666
25 pages
arxiv created 2011/02/23 · openalex publication_date 2011/02/23 · arxiv updated 2011/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs and non linear partial differential equations (PDEs in short) and hence enables to solve high dimensional non linear PDEs. In this work, we apply it to the pricing and hedging of American options in high dimensional local volatility models, which remains very computationally demanding. We have tested our algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear speedups which proves the scalability of our implementation