A Dynamic Model for Credit Index Derivatives

TL;DR

This paper introduces a comprehensive dynamic model for credit index derivatives that captures complex features like volatility, jumps, and counterparty risk, providing closed-form pricing formulas and calibration to market data.

Contribution

It presents a novel top-down affine model with dynamic loss intensity, enabling efficient pricing and calibration of various credit derivatives including CDS, CDO tranches, and index swaptions.

Findings

Closed-form formulas for index CDS, CDO tranches, and Nth-to-default

Exact and approximate pricing methods for index swaptions

Successful calibration to 2009 market data

Abstract

We present a new model for credit index derivatives, in the top-down approach. This model has a dynamic loss intensity process with volatility and jumps and can include counterparty risk. It handles CDS, CDO tranches, Nth-to-default and index swaptions. Using properties of affine models, we derive closed formulas for the pricing of index CDS, CDO tranches and Nth-to-default. For index swaptions, we give an exact pricing and an approximate faster method. We finally show calibration results on 2009 market data.