Construction of Martingale Measure in the Hazard Process Model of Credit Risk

TL;DR

This paper constructs a martingale measure within the hazard process model of credit risk, establishing conditions under which discounted prices become martingales, thus addressing a key assumption in credit risk modeling.

Contribution

It provides a constructive method to establish the existence of an equivalent martingale measure under minimal no-arbitrage conditions in credit risk models.

Findings

Successfully constructs a martingale measure in the hazard process framework.

Identifies weak no-arbitrage conditions necessary for measure construction.

Ensures discounted prices of stocks and bonds are martingales under the new measure.

Abstract

In credit risk literature, the existence of an equivalent martingale measure is stipulated as one of the main assumptions in the hazard process model. Here we show by construction the existence of a measure that turns the discounted stock and defaultable bond prices into martingales by identifying a no-arbitrage condition, in as weak a sense as possible, which facilitates such a construction.