Branching Diffusions with Jumps and Valuation with Systemic Counterparties

29 Pages Posted: 11 Sep 2019 Last revised: 14 Jan 2020

See all articles by Christoph Belak

Christoph Belak

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften

Daniel Hoffmann

University of Trier

Frank Thomas Seifried

University of Trier

Date Written: January 14, 2020

Abstract

We extend the branching diffusion Monte Carlo method of Henry-Labordère e.a. [2019] 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

Suggested Citation

Belak, Christoph and Hoffmann, Daniel and Seifried, Frank Thomas, Branching Diffusions with Jumps and Valuation with Systemic Counterparties (January 14, 2020). Available at SSRN: https://ssrn.com/abstract=3451280 or http://dx.doi.org/10.2139/ssrn.3451280

Christoph Belak (Contact Author)

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften ( email )

Institut fur Mathematik, Sekr. MA 7-1
Strasse des 17. Juni 136
Berlin, 10623
Germany

Daniel Hoffmann

University of Trier ( email )

15, Universitaetsring
Trier, 54286
Germany

Frank Thomas Seifried

University of Trier ( email )

Department IV - Mathematics
Universitätsring 19
Trier, 54296
Germany

HOME PAGE: http://sites.google.com/site/seifriedfinance/

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