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.

Cited by in corpus (8)

• Solving high-dimensional partial differential equations using deep learning
• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
• On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations
• Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE
• Multi-level Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities
• Novel multi-step predictor-corrector schemes for backward stochastic differential equations
• Large Deviations for SDE driven by Heavy-tailed Lévy Processes
• An FBSDE Approach to American Option Pricing with an Interacting Particle Method