Generic Lévy One-factor Models for the Joint Modelling of Prepayment and Default: Modelling LCDX

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Generic Lévy One-factor Models for the Joint Modelling of Prepayment and Default: Modelling LCDX

by Péter Dobránszky of Finalyse SA, FORTIS Bank & Katholieke Universiteit Leuven, and
Wim Schoutens of Katholieke Universiteit Leuven

July 29, 2008

Abstract: In this paper, we introduce a new robust model for modelling and pricing LCDX tranches. We extend the generic one-factor model of Albrecher, Ladoucette, & Schoutens (2007), which was developed for modelling and pricing of a synthetic CDO of CDSs, to a model for tranched portfolio of loan-only CDSs (LCDSs). The essential difference is that now also the possibility of prepayments is built in. As a main advantage, the proposed model allows to trade LCDX tranches expressed in base correlations.

JEL Classification: G10, G12, G13, G15, G20, G21.

Keywords: LCDX tranches, LCDS, loan-only credit default swap, credit risk, credit derivatives, one-factor model, base correlations, tranche pricing, recursive formula, Lévy processes, default risk, prepayment risk, alpha-stable process, variance gamma process.

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