Bivariate Semi-Markov Process for Counterparty Credit Risk

TL;DR

This paper introduces a multivariate semi-Markov model to better capture the non-Markovian dynamics of credit rating migrations in counterparty credit risk, improving risk assessment and derivative pricing.

Contribution

It develops a novel multivariate semi-Markov chain framework for credit risk modeling, addressing limitations of traditional Markov models in capturing credit rating dynamics.

Findings

Provides methods for computing transition probabilities

Derives reliability functions for credit ratings

Offers a new approach to pricing Credit Default Swaps

Abstract

We consider the problem of constructing an appropriate multivariate model for the study of the counterparty credit risk in credit rating migration problem. For this financial problem different multivariate Markov chain models were proposed. However the markovian assumption may be inappropriate for the study of the dynamic of credit ratings which typically show non markovian like behaviour. In this paper we develop a semi-Markov approach to the study of the counterparty credit risk by defining a new multivariate semi-Markov chain model. Methods are given for computing the transition probabilities, reliability functions and the price of a risky Credit Default Swap.