CDO term structure modelling with Levy processes and the relation to market models

TL;DR

This paper develops a top-down CDO model driven by Levy processes, establishing arbitrage-free conditions and connecting it to market models through a forward rate framework.

Contribution

It generalizes existing models by incorporating Levy processes and links them to market models, providing new insights into arbitrage conditions and model relations.

Findings

Derived conditions for absence of arbitrage

Embedded market models within the Levy-driven framework

Extended the forward rate approach to CDO modeling

Abstract

This paper considers the modelling of collateralized debt obligations (CDOs). We propose a top-down model via forward rates generalizing Filipovi\'c, Overbeck and Schmidt (2009) to the case where the forward rates are driven by a finite dimensional L\'evy process. The contribution of this work is twofold: we provide conditions for absence of arbitrage in this generalized framework. Furthermore, we study the relation to market models by embedding them in the forward rate framework in spirit of Brace, Gatarek and Musiela (1997).