A nested MLMC framework for efficient simulations on FPGAs
Journal:
arXiv
Published Date:
Feb 10, 2025
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.
