Valuation of Loan CDS and Synthetic Loan CDO with Prepayment Risk

by Michael Hong Liang of Industrial Bank (China) Co., LTD.

March 23, 2009

Abstract: We have presented a simple model to price LCDS and synthetic Loan CDO with prepayment risk. The implementation is still in one-factor semi-analytic, which facilitates fast and accurate risk calculations. The model is flexible and stable, and is able to fit exactly the market prices of all the LCDX tranches including the 15-100% supper senior tranche. The prepayment rate parameter in the model is well behaved and the impact on correlation is simple and intuitive. The higher the prepayment rate the lower the correlation. For a given strike the relationship between correlation and prepayment rate is approximately linear. We back tested the model for a period of time using market LCDX9 data, the model parameters, base correlations and prepayment rates, are mostly stable from day-to-day.

JEL Classification: G13.

Keywords: CLO, CDO valuation, structured credit, prepayment risk.

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