Summary
This empirical paper investigates the effect of different distributional assumptions governing defaultable bond price uncertainty on the price of a credit default swap. We value a credit default swap using the two-factor Hull-White (1994) model for the term structure of default-free Spot interest rates and the credit spread process of a Baa-rated bond index and use the fractional recovery model of Duffie-Singleton (1999) and its multiple default extension as given in Schönbucher (1996,1998). The model is implemented using a tree algorithm outlined in Schönbucher (1999) where one factor is used for the spot interest rate and the other factor is for the credit spread or the intensity rate of a Cox process. This tree representation permits correlation between the spot rate and the credit spread dynamics of the Baa bond index, enabling us to provide a model that better fits the term structure of default-free and defaultable bond prices. We compare the values of a credit default swap obtained when the underlying risk factors are modeled with Gaussian and stable non-Gaussian distributions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Altman, E.I. (1983/1990). Corporate Financial Distress. Wiley, New York.
Altman, E.I., Brady, B., Resti, A., Sironi, A. (2002). The link between default and recovery rates: Implications for credit risk models and procylicality.
Anson, M.J.P. (1999). Credit Derivatives. Frank J. Fabozzi Associates, New Hope, Pennsylvania
Artzner, P., and Delbaen, F. (1992). Credit risk and prepayment option. 22:81-96.
Bakshi, G., Madan, D., Zhang, F. (2001). Recovery in default risk modeling: Theoretical foundations and empirical applications. University of Maryland and the Federal Reserve Board.
Black, F., and Cox., J. (1976). Valuing corporate securities: Some effects of bond indenture provisions. Journal of Finance, 351-367.
Black, F., and Scholes, M. (1973).The pricing of options and corporate liabilities. Journal of Political Economy, 81 : 637–654.
Bremaud, Pierre. (1981). Point Processes and Queues. Springer, Berlin, Heidelberg, New York.
Clewlow, L., Strickland, Chris. (1998). Implementing Derivatives Models. Wiley Series in Financial Engineering.
Das, S.R. (1995). Credit risk derivatives. Journal of Derivatives, 2(3):7–23.
Duffie, D. (1998). Defaultable term structure models with fractional recovery of par. Working paper, Graduate School of Business, Stanford University.
Duffie, D. (1994). Forward rate curves with default risk. Working paper, Graduate School of Business, Stanford University.
Duffie, D. (1999). Credit swap valuation. Working paper, Graduate School of Business, Stanford University.
Duffie, D., and Huang, M. (1996).Swap rates and credit quality. Journal of Finance, 51:921–949.
Duffie, D., Schröder, M., and Skiadas, C. (1996). Recursive valuation of defaultable securities and the Urning of resolution of uncertainty. Annais of Probability 6, 1075–1090.
Duffie, D., and Singleton. K. (1997). An econometric model ofthe term structure of interest rate swap yields. Journal of Finance, 52(4):1287–1322.
Duffie, D., and K. Singleton. (1999). Modeling term structures of defaultable bonds. The Review of Financial Studies, 12(4):687–720.
Embrechts, P., Klüppelberg, C., Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. Springer Verlag, Berlin.
Flesaker, B., Houghston, L., Schreiber, L., and Sprung, L. Taking all the credit. Risk Magazine, 7:105–108.
Fons, J.S. (1994).Using default rates to model the term structures of defaultable bonds. Financial Analysts Journal, September-October, 25–32
Franks, J.R. and Torous, W.N. (1994). A comparison of financial re-contracting in distressed exchanges and Chapter 11 reorganizations. Journal of Financial Economics, 35 349–370
Geske, R. The valuation of corporate liabilities as Compound options.
Gupton, G.M. and Stein, R.M. (2002). LossCalc™ Moody’s Model for predicting loss given default (LGD), Global Credit Research, Moody’s Investor Services.
Heath, D., Jarrow, R., and Morton, A. (1992 ) Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 60:77–105
Hull, J.C. (2000). Options, Futures, and Other Derivatives. Prentice-Hall International.
Hull, J. and A. White. (1990).Pricing Interest-Rate-Derivative Securities. Review of Financial Studies, 3, 573–592.
Hull, J. and A. White. (1994a). Numerical procedures for implementing term structure models I: Single-Factor models. Journal of Derivatives, 2, 7–16.
Hull, J. and A. White. (1994b). Numerical procedures for implementing term structure models II: Two-Factor models. Journal of Derivatives, 2, 37–48.
Jarrow, R.A., Lando, D., and Turnbull, S.M. (1993, revised 1994). A Markov model for the term structure of credit risk spreads. Working paper, Johnson Graduate School of Management, Cornell University.
Jarrow, R.A., and Stuart M. Turnbull. (1995).Pricing derivatives on financial securities subject to credit risk. Journal of Finance, 50, 53–85.
Jarrow, R.A. and Turnbull, S.M. (2000).The intersection of market and credit risk. Journal of Banking and Finance 24, 271–299.
Jarrow, R.A. and Yildirim, Y. (2002). Valuing default swaps under market and credit risk correlation. The Journal of Fixed Income, 7–19.
Lando, D. (1994). Three essays on contingent claims pricing. Ph.D. thesis, Graduate School of Management, Cornell University.
Lando, D. (1998). On Cox processes and credit risky securities. Review of Derivatives Research, 2, (2/3) 99–120.
Longstaff, F.A., and Schwartz, E. (June 1995). The pricing of credit derivatives. Journal of Fixed Income, 5(1):6–14.
Madan, D and H. Unal. (1998).Pricing the risks of default. Review of Derivatives Research, 2 (2/3) 121–160.
Mandelbrot, B.B., (1963). The Variation of certain speculative prices. Journal of Business 26, 394–419.
Mandelbrot, B.B., (1967).The Variation of some other speculative prices. Journal of Business 40, 393–413.
Maxtin, B., Rachev, S.T., Schwartz, E.S. (2000). Stable non-Gaussian models for credit risk management. Working paper, University of Karlsruhe, Germany.
Merton, R.C.(1974). On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29:449–470.
Mittnik, S., Rachev, S.T., Doganoglu, T. and Chenyao, D. (1996) Maximum likelihood estimation of stable Paretian models. Working paper, Christian Albrechts University, Kiel.
Mittnik, S., Rachev, S.T., (2000). Diagnosing and treating the fat tails in financial returns data. Journal of Empirical Finance 7, 389–416
Paulauskas, V. and Rachev, S.T. (1999 ). Maximum likelihood estimators in regression models with infinite variance innovation. Working paper, Vilnius University, Lithuania
Prigent, J.L., Renault, O., Scaillet, O. (2001). An empirical investigation in credit spread indices
Rachev, S.T., (1991). Probability Metrics and the Stability of Stochastic Models. John Wiley & Sons, Chichester, New York.
Rachev, S.T., Mittnik, S. (2000). Stable Paretian Models in Finance. Wiley & Sons, New York.
Rachev, S.T., Racheva-Jotova, B., Hristov, B., I. Mandev (1999). Software Package for Market Risk (VaR) Modeling for Stable Distributed Financial Distributed Returns Mercury 1.0 Documentation.
Rachev, S.T., Schwartz, E., Khindanova, I., (2000). Stable modeling of credit risk. Working paper UCLA.
Rachev, S.T., Tokat, Y. (2000) Asset and liability management: recent advances. CRC Handbook on Analytic Computational Methods in Applied Mathematics.
Samorodnitsky, G., Taqqu, M.S. (1994). Stable Non-Gaussian Random Variables. Chapman and Hall, New York.
Schönbucher, P. (August 1996). The term structure of defaultable bond prices. Discussion Paper B-384, University of Bonn, SFB 303.
Schönbucher, P. (1998). Term structure modelling of defaultable bonds. Discussion Paper B-384, University of Bonn, SFB 303. Review of Derivatives Studies, special Issue : Credit Risk 2 (2/3), 161-192.
Schönbucher, P. (1999). Credit Risk Modelling and Credit Derivatives. Ph.D.-.thesis, Faculty of Economics, Bonn University.
Schönbucher, P. (June 1999). A tree implementation of a credit spread model for credit derivatives. Department of Statistics, Bonn University.
Tavakoli, Janet M. (1998). Credit Derivatives: A guide to instruments and applications. John Wiley Sz Sons.
Tokat, Y., Rachev, S.T., Schwartz, E.S. (2001). Asset Liability Management: A review and some new results in the presence of heavy tails. Ziemba, W.T. (Ed)Handbook of Heavy Tailed Distributions in Finance, Handbook of Finance.
Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–188
Wilson, T. (1997a). Portfolio credit risk (1). Risk 10 (9) 111–116.
Wilson, T. (1997b).Portfolio credit risk (2). Risk 10 (10) 56–61.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
D’Souza, D., Amir-Atefi, K., Racheva-Jotova, B. (2003). Valuation of a Credit Default Swap: The Stable Non-Gaussian versus the Gaussian Approach. In: Bol, G., Nakhaeizadeh, G., Rachev, S.T., Ridder, T., Vollmer, KH. (eds) Credit Risk. Contributions to Economics. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-59365-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-59365-9_3
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-0054-8
Online ISBN: 978-3-642-59365-9
eBook Packages: Springer Book Archive