Pathwise CVA Regressions With Oversimulated Defaults

Lokman Abbas-Turki, Stéphane Crépey () and Bouazza Saadeddine ()
Additional contact information
Stéphane Crépey: UFR Mathématiques UPCité - UFR Mathématiques [Sciences] - Université Paris Cité - UPCité - Université Paris Cité, LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité

Post-Print from HAL

Abstract: We consider the computation by simulation and neural net regression of conditional expectations, or more general elicitable statistics, of functionals of processes (X, Y). Here an exogenous component Y (Markov by itself) is time-consuming to simulate, while the endogenous component X (jointly Markov with Y) is quick to simulate given Y , but is responsible for most of the variance of the simulated payoff. To address the related variance issue, we introduce a conditionally independent, hierarchical simulation scheme, where several paths of X are simulated for each simulated path of Y. We analyze the statistical convergence of the regression learning scheme based on such block-dependent data. We derive heuristics on the number of paths of Y and, for each of them, of X, that should be simulated. The resulting algorithm is implemented on a graphics processing unit (GPU) combining Python/CUDA and learning with PyTorch. A CVA case study with a nested Monte Carlo benchmark shows that the hierarchical simulation technique is key to the success of the learning approach.

Keywords: hierarchical simulation; neural net regression; machine learning; X-valuation adjustment (XVA) (search for similar items in EconPapers)
Date: 2023
Note: View the original document on HAL open archive server: https://hal.science/hal-03910149v1
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Mathematical Finance, inPress, ⟨10.1111/mafi.12368⟩

Downloads: (external link)
https://hal.science/hal-03910149v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03910149

DOI: 10.1111/mafi.12368

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().