Interacting Default Intensity with Hidden Markov Process

TL;DR

This paper introduces a credit risk model combining default intensity with a hidden Markov process, providing a filtering method to estimate the underlying state and deriving joint default time distributions for practical financial applications.

Contribution

It presents a novel reduced-form credit risk model with a hidden Markov process and derives closed-form joint distributions of default times without restrictive assumptions.

Findings

Derived closed-form distributions for multiple default times

Developed a filtering method for hidden Markov states

Applied formulas to credit derivative pricing and hedging

Abstract

In this paper we consider a reduced-form intensity-based credit risk model with a hidden Markov state process. A filtering method is proposed for extracting the underlying state given the observation processes. The method may be applied to a wide range of problems. Based on this model, we derive the joint distribution of multiple default times without imposing stringent assumptions on the form of default intensities. Closed-form formulas for the distribution of default times are obtained which are then applied to solve a number of practical problems such as hedging and pricing credit derivatives. The method and numerical algorithms presented may be applicable to various forms of default intensities.