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

34 Pages Posted: 30 Aug 2012

See all articles by Ernst Eberlein

Ernst Eberlein

University of Freiburg

Zorana Grbac

Université Paris VII Denis Diderot

Thorsten Schmidt

University of Freiburg

Date Written: July 19, 2012

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

Suggested Citation

Eberlein, Ernst and Grbac, Zorana and Schmidt, Thorsten, Market Models for Credit Risky Portfolios Driven by Time-Inhomogeneous Levy Processes (July 19, 2012). Available at SSRN: https://ssrn.com/abstract=2137607 or http://dx.doi.org/10.2139/ssrn.2137607

Ernst Eberlein

University of Freiburg ( email )

Department of Mathematical Stochastics
Eckerstrasse 1
D-79104, Freiburg
Germany
++49 761 203 5660 (Phone)
++49 761 203 5661 (Fax)

Zorana Grbac

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005
France

Thorsten Schmidt (Contact Author)

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

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