Valuation of a Tranched Loan Credit Default Swap Index

Jin Liang, Yujing Zhou

.

DOI: 10.4236/ti.2011.24025                

Abstract

This paper provides a methodology for valuing a Loan Credit Default Swap Index (LCDX) and its tranches involving both default and prepayment risks. The valuation is path dependence, where interest, default and prepayment rates are correlated stochastic processes following CIR processes. By Monte Carlo simulation, a numerical solution and team structure of tranched LCDX are obtained. Computing examples are provided.

Keywords

LCDX, Default, Prepayment, Monte Carlo Method

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. Merton, “On the Valuation of Corporate Debt: the Risk Structure of Interest Rates,” Journal of Finance, Vol. 29, No. 2, 1974, pp. 449-470. doi:10.2307/2978814
[2]	F. Black and J. Cox, “Valuing Corporate Securities: Some Effects of Bond Indenture Provisions,” Journal of Finance, Vol. 31, No. 2, 1976, pp. 351-367. doi:10.2307/2326607
[3]	F. Longstaff and E. Schwartz, “A Simple Approach to Valuate Risky Fixed and Floating Rate Debt,” Journal of Finance, Vol. 50, No. 3, 1995, pp. 789-819. doi:10.2307/2329288
[4]	D. Duffie and K. J. Singleton, “Modeling Term Structure of Defaultable Bonds,” Review of Financial Studies, Vol. 12, No. 4, 1999, pp. 687-720. doi:10.1093/rfs/12.4.687
[5]	D. Lando, “On Cox Processes and Credit Risky Securities,” Review of Derivatives Research, Vol. 2, No. 2-3, 1998, pp. 99-120. doi:10.1007/BF01531332
[6]	C. Zhou, “An Analysis of Default Correlation and Multiple Defaults,” Review of Financial Studies, Vol. 14, No. 2, 2001, pp. 555-576. doi:10.1093/rfs/14.2.555
[7]	W. Zhen, “Valuation of Loan CDS under Intensity Based Model,” Working Paper, Stanford University, 2007.
[8]	P. Dobranszky, “Joint Modeling of CDS and LCDS Spreads with Correlated Default and Prepayment Intensities and with Stochastic Recovery Rate,” Technical Report 08-04, Section of Statistics, Leuven, 2008.
[9]	K. Giesecke, “Portfolio Credit Risk: Top Down vs. Bottom Up Approaches,” In: R. Cont, Ed., Frontiers in Quantitative Finance: Credit Risk and Volatility Modeling, John Wiley & Sons, Chichester, 2008.
[10]	S. Wu, L. S. Jiang and J. Liang, “Pricing of Mortgage-Backed Securities with Repayment Risk,” Working Paper, 2008.
[11]	H. Shek, S. Uematsu and W. Zhen, “Valuation of Loan CDS and CDX,” Working Paper, Stanford University. 2007.
[12]	P. Dobranszky and W. Schoutens, “Generic Levy One-Factor Models for the Joint Modeling of Prepayment and Default: Modeling LCDX,” Technical Report 08-03, Section of Statistics, Leuven, 2008.
[13]	J. Liang and Y. J. Zhou, “Valuation of a Basket Loan Credit Default Swap,” International Journal of Financial Research, Vol. 12, 2010, pp. 21-29.
[14]	L. S. Jiang, “Mathematical Modeling and Cases Analysis of Financial Derivative Pricing,” Higher Education Press, Beijing, 2008.
[15]	V. Linetsky, “Computing Hitting Time Densities for CIR and OU Diffusions: Applications to Mean-Reverting Models,” Journal of Computational Finance, Vol. 7, No. 4, 2004, pp. 1-22.