Generic Levy One-Factor Models for the Joint Modelling of Prepayment and Default: Modelling LCDX

Abstract

In this paper, we introduce a new robust model for modelling and pricing LCDX tranches. We extend the generic one-factor model of [1], 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.

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

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