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.

翻译：多级蒙特卡洛方法通过结合多分辨率随机微分方程近似，降低了金融期权定价的总计算成本。本文探索了通过在使用可配置硬件设备（如现场可编程门阵列）时采用低精度计算来进一步降低成本并提高能效的途径。我们提出了一种新框架，该框架利用近似随机变量和经优化精度的定点运算，以较低成本生成大多数随机微分方程路径，从而降低多级蒙特卡洛框架的总成本。我们首先讨论了多种低成本生成近似正态随机增量的方法。随后，为设定路径生成中变量的位宽，我们提出了舍入误差模型，并优化了每个多级蒙特卡洛层级上所有变量的精度。通过这些关键改进，我们提出的框架比现有的混合精度多级蒙特卡洛框架提供了更高的计算节省。