Counterparty Risk Valuation: A Marked Branching Diffusion Approach

Abstract

The purpose of this paper is to design an algorithm for the computation of the counterparty risk which is competitive in regards of a brute force Monte-Carlo of Monte-Carlo method (with nested simulations). This is achieved using marked branching diffusions describing a Galton-Watson random tree. Such an algorithm leads at the same time to a computation of the (bilateral) counterparty risk when we use the default-risky or counterparty-riskless option values as mark-to-market. Our method is illustrated by various numerical examples.

Keywords: counterparty risk valuation, branching diffusions, Galton-Watson tree, BSDE, super-diffusion, semi-linear PDE

JEL Classification: C00, G13