# An Explicit Default Contagion Model and Its Application to Credit Derivatives Pricing

## TL;DR

This paper introduces a new credit default model incorporating macroeconomic factors and contagion effects, providing explicit pricing formulas for CDOs and demonstrating the significance of systematic risk and contagion in default risk.

## Contribution

The paper develops a set-valued Markov chain model for defaults, deriving explicit pricing formulas for CDOs and calibrating the model with market data.

## Key findings

- Systematic default risk and contagion are major contributors to total default risk.
- The model accurately prices CDO tranche spreads using market data.
- Contagion effects significantly impact credit risk assessments.

## Abstract

We propose a novel credit default model that takes into account the impact of macroeconomic information and contagion effect on the defaults of obligors. We use a set-valued Markov chain to model the default process, which is the set of all defaulted obligors in the group. We obtain analytic characterizations for the default process, and use them to derive pricing formulas in explicit forms for synthetic collateralized debt obligations (CDOs). Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support that systematic default risk coupled with default contagion could have the leading component of the total default risk.