GPGPUs in computational finance: Massive parallel computing for American style options

TL;DR

This paper introduces a parallelizable quantization method for pricing American options using GPGPUs, significantly accelerating computations compared to traditional serial CPU approaches.

Contribution

The paper presents a novel parallelization approach for American option pricing, enabling efficient GPU implementation of quantization methods for stochastic processes.

Findings

Significant speed-up with GPU implementation over CPU.

Effective parallelization of conditional expectation computation.

Enhanced memory utilization for faster computations.

Abstract

The pricing of American style and multiple exercise options is a very challenging problem in mathematical finance. One usually employs a Least-Square Monte Carlo approach (Longstaff-Schwartz method) for the evaluation of conditional expectations which arise in the Backward Dynamic Programming principle for such optimal stopping or stochastic control problems in a Markovian framework. Unfortunately, these Least-Square Monte Carlo approaches are rather slow and allow, due to the dependency structure in the Backward Dynamic Programming principle, no parallel implementation; whether on the Monte Carlo levelnor on the time layer level of this problem. We therefore present in this paper a quantization method for the computation of the conditional expectations, that allows a straightforward parallelization on the Monte Carlo level. Moreover, we are able to develop for AR(1)-processes a further parallelization in the time domain, which makes use of faster memory structures and therefore maximizes parallel execution. Finally, we present numerical results for a CUDA implementation of this methods. It will turn out that such an implementation leads to an impressive speed-up compared to a serial CPU implementation.