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Joint Modelling of CDS and LCDS Spreads with Correlated Default and Prepayment Intensities and with Stochastic Recovery Rate

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

November 13, 2008

Abstract: In this paper, we develop and experiment an intensity based multi-factor model, which incorporates the joint modelling of default, prepayment and recovery risks. In this way, the model provides a link between the credit default swap (CDS) and the loan-only credit default swap (LCDS) markets. The purpose of this paper is to analyse the relationship of the CDS and LCDS markets, and find stochastic risk factors that can explain the joint puzzle of CDS and LCDS spreads. The developed model is simple and analytically tractable, but it is able to capture the most often mentioned characteristics of the markets, namely there is negative correlation between the default and prepayment intensities and also there is positive correlation between the default intensity and the loss given default.

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

Keywords: CDS, credit default swap, LCDS, loan-only credit default swap, pricing, valuation, credit derivatives, credit risk, default risk, prepayment risk, recovery risk, correlated default and prepayment intensities, stochastic recovery rate, continuous time modelling, affine processes, multivariate Ornstein-Uhlenbeck process, Riccati ODE.

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