Counterparty Risk Valuation: A Marked Branching Diffusion Approach

By Pierre Henry-Labordère. 2012

77 citations recorded by the source corpus.

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.

Subfields: Demography, Finance

View Paper: https://www.semanticscholar.org/paper/5b5dbd56fc7ed92e68ac66dd7746029127917f10

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Demography

1. Arnulf Jentzen
2. Huyen Pham
3. W. E
4. Idris Kharroubi
5. Martin Hutzenthaler
6. Philippe von Wurstemberger
7. Jiequn Han
8. Xuerong Mao

In Finance

1. Arnulf Jentzen
2. Jiequn Han
3. Idris Kharroubi
4. W. E
5. Huyen Pham
6. Martin Hutzenthaler
7. Philippe von Wurstemberger
8. Xuerong Mao

Citations in the corpus

• Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations (2017, unknown): “, [53, 54, 55, 77, 102, 108]), and probabilistic representations based on extensions of the classical Feynman-Kac formula (cf.”
• Feynman-Kac representation for Hamilton-Jacobi-Bellman IPDE (2012, methodology): “An alternative and promising approach, left for future research, would be to apply a forward Monte-Carlo scheme on the penalized semi-linear PDE by means of marked branching regime switching diffusion and interacting particle methods, as recently proposed in [11].”
• Solving high-dimensional partial differential equations using deep learning (2017, methodology): “The branching diffusion method has been proposed in [12, 13], which exploits the fact that solutions of semilinear PDEs with polynomial nonlinearity can be represented as an expectation of a functional of branching diffusion processes.”
• Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations (2017, methodology): “, [17, 19, 18] for analytical and numerical results for the Branching diffusion method in the literature).”
• Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks (2019, methodology): “, [16, 53, 55, 56, 75, 88, 93, 98, 101] for probabilistic approximation methods for PDEs using branching diffusions processes, cf.”