Branching Diffusions with Jumps and Valuation with Systemic Counterparties

Christoph Belak, Daniel Hoffmann and Frank T. Seifried

No 2020-04, Working Paper Series from University of Trier, Research Group Quantitative Finance and Risk Analysis

Abstract: We extend the branching diffusion Monte Carlo method of Henry-Labordere e.a.[11] to the case of parabolic PDEs with mixed local-nonlocal analytic nonlinearities. We investigate branching diffusion representations of classical solutions, and we provide suficient conditions under which the branching diffusion representation solves the PDE in the viscosity sense. Our theoretical setup directly leads´to a Monte Carlo algorithm, whose applicability is showcased in a stylized high-dimensional example. As our main application, we demonstrate how the methodology can be used to value financial positions with defaultable, systemically important counterparties.

Keywords: Branching Diffusion; Mixed Local-Nonlocal PDE; Nonlinear Jumps; Monte Carlo Simulation; Credit Valuation Adjustment (search for similar items in EconPapers)
JEL-codes: C02 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:trr:qfrawp:202004

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