Branching Diffusions with Jumps and Valuation with Systemic Counterparties
29 Pages Posted: 11 Sep 2019 Last revised: 14 Jan 2020
Date Written: January 14, 2020
We extend the branching diffusion Monte Carlo method of Henry-Labordère e.a.  to the case of parabolic PDEs with mixed local-nonlocal analytic nonlinearities. We investigate branching diffusion representations of classical solutions, and we provide sufficient 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
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