Efficient parallel Monte-Carlo techniques for pricing American options including counterparty credit risk

Abstract

In this article we mainly propose a numerical scheme, based on the novel Stochastic Grid Bundling Method (SGBM), to price American options in the presence of counterparty credit risk. More precisely, we consider the regression techniques (regress later) employed in the SGBM method and take advantage of the bundling structure to develop an efficient parallel strategy that is implemented on a GPU architecture. Also, a novel interpolation-based technique is efficiently applied in the XVA computation. Besides the advantages obtained in the sequential version, when compared with the more classical Least Squares Method, we show the relevant speedup of the parallel GPU-based version with respect to the sequential CPU-based one.

Keywords:

• Counterparty credit risk
• Total value adjustment
• American options
• Monte Carlo methods
• GPU computing

2020 AMS Subject Classifications:

• 65C05
• 65C30
• 65Y05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The abbreviation derives from the fact that the method employs cosine series expansions to estimate the underlying density function.

2 Values which ensure a sufficiently high precision

Additional information

Funding

Í. Arregui, Á. Leitao, B. Salvador and C. Vázquez were funded by Spanish Ministry of Science and Innovation with [grant number PID2019-108584RB-I00]. Á. Leitao acknowledges the financial support from the Spanish Ministry of Science and Innovation, through the Juan de la Cierva-formación 2017 (FJC17) grant in the framework of the national programme for R&D 2013–2016. The authors wish to acknowledge the support received from the Centro de Investigación en Tecnologías de la Información y las Comunicaciones de Galicia, CITIC, funded by Xunta de Galicia and the European Union (European Regional Development Fund, Galicia 2014–2020 Program) by [grant number ED431G 2019/01]. Also the authors acknowledge the funding by Xunta de Galicia through [grant numbers ED431C2018/033 and ED431C 2022/47].