Market Models for CDOs Driven by Time-inhomogeneous Lévy Processes

by Ernst Eberlein of the University of Freiburg,
Zorana Grbac of the University of Freiburg, and
Thorsten Schmidt of Chemnitz University of Technology

June 10, 2010

Abstract: This paper considers a top-down approach for CDO valuation and proposes a market model. We extend previous research on this topic in two directions: on the one side, we use as driving process for the interest rate dynamics a time-inhomogeneous Lévy process, and on the other side, we do not assume that all maturities are available in the market. Only a discrete tenor structure is considered, which is in the spirit of the classical Libor market model. We create a general framework for market models based on multidimensional semimartingales. This framework is able to capture dependence between the default-free and the defaultable dynamics, as well as contagion effects. Conditions for absence of arbitrage and valuation formulas for tranches of CDOs are given.

JEL Classification: C02, C51, G12.

AMS Classification: 60E10, 60G09, 60J75, 60H20, 62P05, 91B70, 91G40.

Keywords: collateralized debt obligations, loss process, single tranche CDO, top-down model, market model, time-inhomogeneous Lévy processes, Libor rate, forward measuree.

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