Market Models for Credit Risky Portfolios Driven by Time-Inhomogeneous Levy Processes

Abstract

The goal of this paper is to specify market models for credit portfolios in a top-down setting driven by time-inhomogeneous Levy processes. We provide a new framework, conditions for absence of arbitrage, explicit examples, an affine setup which includes contagion and pricing formulas for STCDOs and options on STCDOs. A calibration to iTraxx data with an extended Kalman filter shows an excellent fit over the full observation period. The calibration is done on a set of CDO tranche spreads ranging across six tranches and three maturities.

Keywords: collateralized debt obligations, loss process, single tranche CDO, top-down model, market model, time-inhomogeneous Levy processes, Libor rate, forward measure, affine processes, extended Kalman filter, iTraxx

JEL Classification: G13, C60