GPU acceleration of the stochastic grid bundling method for early-exercise options

Abstract

In this work, a parallel graphics processing units (GPU) version of the Monte Carlo stochastic grid bundling method (SGBM) for pricing multi-dimensional early-exercise options is presented. To extend the method's applicability, the problem dimensions and the number of bundles will be increased drastically. This makes SGBM very expensive in terms of computational costs on conventional hardware systems based on central processing units. A parallelization strategy of the method is developed and the general purpose computing on graphics processing units paradigm is used to reduce the execution time. An improved technique for bundling asset paths, which is more efficient on parallel hardware is introduced. Thanks to the performance of the GPU version of SGBM, a general approach for computing the early-exercise policy is proposed. Comparisons between sequential and GPU parallel versions are presented.

An SGBM-XVA demonstrator: a scalable Python tool for pricing XVA

“…For further details, the readers are referred to our previous work [1]. Furthermore, we will describe a parallel computing version of SGBM, which is a follow-up on [10], in which parallel SGBM was applied to the pricing of multi-dimensional Bermudan options.…”

“…One way to improve the efficiency of the SGBM algorithm is by means of GPU acceleration, which has been successfully implemented for the SGBM algorithm for early-exercise options in [10]. The framework of parallel computation from [10] can also be used for the SGBM solver of BSDEs. In this framework, we divide the SGBM algorithm in two stages, namely, the forward simulation stage and the backward recursion approximation stage.…”

“…The detailed setting for the numerical test is presented in Table 1. This set of parameters is based on the one used in [10] and it has been adopted here as an easy to scale up problem. The main purpose of the tests is to investigate whether the code can be easily extended to solving high-dimensional problems, so we choose a set of parameters whose properties do not change when we change the dimensionality of the problem.…”

Efficient computation of exposure profiles on real-world and risk-neutral scenarios for Bermudan swaptions

“…For high-dimensional problems, one can either use the equal-number bundling technique along each dimension, as employed in Feng and Oosterlee (2014), or one can project the high-dimensional vector onto a one-dimensional vector and then apply the equal-number bundling technique (see Jain and Oosterlee 2015;Leitao and Oosterlee 2015).…”

Stochastic grid bundling method for backward stochastic differential equations

“…This is the same setting as in [16] but for European options instead of Bermudan options. We again use the equal-partitioning technique and sort the paths in different bundles according to the ordering of the values…”