Credit Risk, Market Sentiment and Randomly-Timed Default

TL;DR

This paper introduces a dynamic credit risk model where bond defaults depend on market factors and partial information, leading to explicit formulas for bond prices, hazard rates, and options influenced by market sentiment.

Contribution

It develops a novel framework linking default times to market factors and information processes, providing explicit formulas for pricing and hazard rates based on perceived market sentiment.

Findings

Explicit bond price formulas derived

Hazard rates are functions of information processes

Options on bonds are priced considering market sentiment

Abstract

We propose a model for the credit markets in which the random default times of bonds are assumed to be given as functions of one or more independent "market factors". Market participants are assumed to have partial information about each of the market factors, represented by the values of a set of market factor information processes. The market filtration is taken to be generated jointly by the various information processes and by the default indicator processes of the various bonds. The value of a discount bond is obtained by taking the discounted expectation of the value of the default indicator function at the maturity of the bond, conditional on the information provided by the market filtration. Explicit expressions are derived for the bond price processes and the associated default hazard rates. The latter are not given a priori as part of the model but rather are deduced and shown to be functions of the values of the information processes. Thus the "perceived" hazard rates, based on the available information, determine bond prices, and as perceptions change so do the prices. In conclusion, explicit expressions are derived for options on discount bonds, the values of which also fluctuate in line with the vicissitudes of market sentiment.