Market Models for CDOs Driven by Time-inhomogeneous LÚvy Processes
by Ernst Eberlein of the University of Freiburg,
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 LÚvy 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.
Keywords: collateralized debt obligations, loss process, single tranche CDO, top-down model, market model, time-inhomogeneous LÚvy processes, Libor rate, forward measuree.