A nested MLMC framework for efficient simulations on FPGAs

Haas Irina-Beatrice () and Giles Michael B. ()
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Haas Irina-Beatrice: Mathematical Institute, University of Oxford, Oxford, United Kingdom
Giles Michael B.: Mathematical Institute, University of Oxford, Oxford, United Kingdom

Monte Carlo Methods and Applications, 2025, vol. 31, issue 3, 173-188

Abstract: Multilevel Monte Carlo (MLMC) reduces the total computational cost of financial option pricing by combining SDE approximations with multiple resolutions. This paper explores a further avenue for reducing cost and improving power efficiency through the use of low precision calculations on configurable hardware devices such as Field-Programmable Gate Arrays (FPGAs). We propose a new framework that exploits approximate random variables and fixed-point operations with optimised precision to generate most SDE paths with a lower cost and reduce the overall cost of the MLMC framework. We first discuss several methods for the cheap generation of approximate random Normal increments. To set the bit-width of variables in the path generation we then propose a rounding error model and optimise the precision of all variables on each MLMC level. With these key improvements, our proposed framework offers higher computational savings than the existing mixed-precision MLMC frameworks.

Keywords: Multilevel Monte Carlo; high-performance computing; FPGAs; fixed-point arithmetic; mixed precision; approximate random number generation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1515/mcma-2025-2010

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