# Dynamical analysis of corporate bonds based on the yield spread term-quality surface

- 55 Downloads

## Abstract

Our aim of this research is to propose a model which estimates implied relative credit reliability from the yield spread of defaultable bonds and evaluates their spread risk. We introduce “yield spread term-quality surface” (YSTQS) which is defined on the space of duration and credit reliability of the issuers, and express their yield spread. First, we review the general pricing theorem of defaultable bonds with unpredictable recovery in the no-arbitrage context based on the external hazard rates. Second, we show that the dynamics of state variables determine the shape of the YSTQS, and they drive the YSTQS if the loss-adjusted hazard rates are described by a function of them. Finally, we show an empirical analysis of our model with daily yield spread, duration, and the credit ratings of corporate bonds.

## Keywords

Default risk Hazard rate Yield spread term-quality surface Credit quality Spread risk Markov state variable No-arbitrage## JEL classifications

C32 C33 C51 G33## Preview

Unable to display preview. Download preview PDF.

## Notes

### Acknowledgements

The author thanks NAKAMURA Nobuhiro, associate professor of Hitotsubashi University, and NAKAGAWA Hidetoshi, associate professor of Tokyo Institute of Technology, for their accurate advises, as well as two anonymous referees for helpful and constructive comments. And we also thank Monique Jeanblanc, professor of Evry University, for stimulating discussions and insightful comments.

## References

- Black, F., & Cox, J. C. (1976). Valuing corporate securities: Some effects of bond indenture provisions.
*Journal of Finance, 31*, 351–367.CrossRefGoogle Scholar - Blanchet-Scallied, C., & Jeanblanc, M. (2004). Hazard rate for credit risk and hedging defaultable contingent claims.
*Finance and Stochastics, 8*, 145–159.CrossRefGoogle Scholar - Bielecki, T., Crepéy, S., Jeanblanc, M., & Rutkowski, M. (2005). Valuation of basket credit derivatives in the credit migrations environment. Working paper.Google Scholar
- Bielecki, T., & Rutkowski, M. (2001).
*Credit risk: Modeling, valuation and hedging*. Springer Finance.Google Scholar - Constantindes, G. M. (1992). A theory of the nominal term structure of interest rates.
*Review of Financial Studies, 5*(4), 531–552.CrossRefGoogle Scholar - Douady, R., & Jeanblanc, M. (2002). A rating-based model for credit derivatives.
*European Investment Review*www.theeir.com.Google Scholar - Duffee, G. R. (1999). Estimating the price of default risk.
*Review of Financial Studies, 12*(1), 197–226.CrossRefGoogle Scholar - Duffie, D., & Kan, R. (1996). A yield-factor model of interest rates.
*Mathematical Finance, 6*, 379–406.CrossRefGoogle Scholar - Duffie, D., & Lando, D. (2001). Term structure of credit spreads with incomplete accounting information.
*Econometrica, 69*, 633–664.CrossRefGoogle Scholar - Duffie, D., & Singleton, K (1999) Modeling term structures of defaultable bonds.
*Review of Financial Studies, 12*, 687–720.CrossRefGoogle Scholar - Farnsworth, H., & Li, T. (2003). Modeling credit spreads and ratings migration. Working paper.Google Scholar
- Feldhütter, P., & Lando, D. (2005). Decomposing swap spreads. Working paper.Google Scholar
- Heath, D., Jarrow, R., & Morton, A. (1992). Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation.
*Econometrica, 60*(1), 77–105.CrossRefGoogle Scholar - Jamshidian, F. (1996). Bond, futures and option valuation in the quadratic interest rate model.
*Applied Mathematical Finance, 3*, 93–115.CrossRefGoogle Scholar - Jarrow, R., Lando, D., & Turnbull, S. (1997). A Markov model for the term structure of credit risk spreads.
*Review of Financial Studies, 10*, 481–523.CrossRefGoogle Scholar - Kusuoka, S. A. (1999). Remark on default risk models.
*Advances in Mathematical Economics, 1*, 69–82.Google Scholar - Merton, R. (1974). On the pricing of corporate debt: The risk structure of interest rates.
*Journal of Finance, 29*, 449–470.CrossRefGoogle Scholar - Protter, P. (2003).
*Stochastic integration and differential equations*(2nd ed.). New York: Springer-Verlag.Google Scholar