Branching Diffusions with Jumps, and Valuation with Systemic Counterparties

36 Pages Posted: 22 Dec 2021

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

Multiple version iconThere are 2 versions of this paper

Date Written: January 16, 2020

Abstract

We extend the branching diffusion Monte Carlo method of Henry-Labordère et al to the case of parabolic partial differential equations 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 partial differential equation in the viscosity sense. Our theoretical setup directly leads to a Monte Carlo algorithm, whose applicability is showcased in the valuation of financial positions with defaultable, systemically important counterparties and a high-dimensional underlying.

Keywords: branching diffusion, mixed local–nonlocal partial differential equations (PDEs), 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 16, 2020). Journal of Computational Finance, Vol. 25, No. 3, 2021, Available at SSRN: https://ssrn.com/abstract=3987956

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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