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An Explicit, Multi-Factor Credit Default Swap Pricing Model with Correlated Factors

Published online by Cambridge University Press:  06 April 2009

Ren-Raw Chen ,
Xiaolin Cheng ,
Frank J. Fabozzi  and
Bo Liu
Ren-Raw Chen
Affiliation:
rchen@rci.rutgers.edu, Rutgers University, Rutgers Business School-New Brunwsick, 94 Rockafeller Road, Piscataway, NJ 08854
Xiaolin Cheng
Affiliation:
xiaolin.cheng@moodys.com, Moody's Investor Service, 7 WTC, 250 Greenwich Street, New York, NY 10007
Frank J. Fabozzi
Affiliation:
frank.fabozzi@yale.edu, Yale University, School of Management, PO Box 20800, New Haven, CT 06520;
Bo Liu
Affiliation:
bo.liu@citi.com, Citigroup Global Market Inc., 390 Greenwich Street, New York, NY 10013.
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Abstract

With the recent significant growth in the single-name credit default swap (CDS) market has come the need for accurate and computationally efficient models to value these instruments. While the model developed by Duffie, Pan, and Singleton (2000) can be used, the solution is numerical (solving a series of ordinary differential equations) rather than explicit. In this paper, we provide an explicit solution to the valuation of a credit default swap when the interest rate and the hazard rate are correlated by using the “change of measure” approach and solving a bivariate Riccati equation. CDS transaction data for the period 2/15/2000 through 4/8/2003 for 60 firms are used to test both the goodness of fit of the model and provide estimates of the influence of economic variables in the market for credit-risky bonds.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 43 , Issue 1 , March 2008 , pp. 123 - 160
Copyright
Copyright © School of Business Administration, University of Washington 2008

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References

Ahn, D. H.; Dittmar, R. F.; and Gallant, A. R. “Quadratic Gaussian Models: Theory and Evidence.” Review of Financial Studies, 15 (2002), 243–288.CrossRefGoogle Scholar
Bakshi, G.; Madan, D.; and Zhang, F. “Understanding the Role of Recovery in Default Risk Models: Empirical Comparisons and Implied Recovery Rates.” Working Paper, University of Maryland (2002).Google Scholar
Berndt, A.; Douglas, R.; Duffie, D.; Ferguson, M.; and Schranz, D. “Measuring Default-Risk Premia from Default Swap Rates and EDFs.” Working Paper, Stanford University (2005).Google Scholar
Boyle, P.; Tian, W.; and Guan, F. “The Riccati Equation in Mathematical Finance.” Journal of Symbolic Computation, 22 (2002), 343–356.CrossRefGoogle Scholar
Chen, R. R., and Huang, J. “Credit Spread Bounds and Their Implications for Credit Risk Modeling.” Working Paper, Rutgers University and Penn State University (2001).CrossRefGoogle Scholar
Chen, R. R., and Yang, T. T. L. “A Simple Multi-factor, Time-dependent-parameter Model for Term Structures of Interest Rates.” Review of Quantitative Finance and Accounting, 19 (2003), 5–20.CrossRefGoogle Scholar
Constantinides, G. M. “A Theory of the Nominal Term Structure of Interest Rates.” Review of Financial Studies, 4 (1992), 531–552.CrossRefGoogle Scholar
Cox, J.; Ingersoll, J.; and Ross, S. A. “A Theory of the Term Structure of Interest Rates.” Econometrica, 53 (1985), 385–407.CrossRefGoogle Scholar
Duffie, D., and Singleton, K. J. “Modeling Term Structure of Defaultable Bonds.” Review of Financial Studies, 12 (1999), 687–720.CrossRefGoogle Scholar
Duffie, D.; Pan, J.; and Singleton, K. J. “Transform Analysis and Asset Pricing for Affine Jump Diffusion.” Econometrica, 68 (2000), 1343–1376.CrossRefGoogle Scholar
Eom, Y. H.; Helwege, J.; and Huang, J. “Structural Models of Corporate Bond Pricing: An Empirical Analysis.” Review of Financial Studies, 17 (2004), 499–544.CrossRefGoogle Scholar
Hull, J.Options, Futures, and Other Derivatives, 5th edNew York, NY: Prentice Hall (2003).Google Scholar
Jamshidian, F. “Pricing of Contingent Claims in the One Factor Term Structure Model.” Working Paper, Merrill Lynch Capital Markets (1987).Google Scholar
Jarrow, R. A., and Turnbull, S.M. “Pricing Derivatives on Financial Securities Subject to Credit Risk.” Journal of Finance, 50 (1995), 53–85.CrossRefGoogle Scholar
Julier, S. J., and Uhlmann, J. K. “A New Extension of the Kalman Filter to Nonlinear Systems.” Proceedings of Aero Sense: The 11th International Symposium on Aerospace/Defense Sensing, Simulation and Controls, Multi Sensor Fusion, Tracking and Resource Management II. SPIE (1997).Google Scholar
Leippold, M., and Wu, L. “Asset Pricing under the Quadratic Class.” Journal of Financial and Quantitative Analysis, 37 (2002), 271–295.CrossRefGoogle Scholar
Longstaff, F. A.; Mithal, S.; and Neis, E. “Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit-Default Swap Market.” Journal of Finance, 66 (2005), 1200–1225.Google Scholar
Scott, L. “The Valuation of Interest Rate Derivatives in a Multi-Factor Term Structure Model with Deterministic Components.” Research Symposium Proceedings. Chicago, IL: Chicago Board of Trade (Winter (1996), I), 223–253.Google Scholar