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An Integral-Equation Approach for Defaultable Bond Prices with Application to Credit Spreads

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Yu-Ting Chen ,
Cheng-Few Lee  and
Yuan-Chung Sheu
Yu-Ting Chen
Affiliation:
National Chiao Tung University
Cheng-Few Lee*
Affiliation:
Rutgers University and National Chiao Tung University
Yuan-Chung Sheu*
Affiliation:
National Chiao Tung University
*
∗∗Postal address: Department of Finance, Rutgers University, New Brunswick, NJ, USA.
∗∗∗Postal address: Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan. Email address: sheu@math.nctu.edu.tw
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Abstract

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We study defaultable bond prices in the Black–Cox model with jumps in the asset value. The jump-size distribution is arbitrary, and following Longstaff and Schwartz (1995) and Zhou (2001) we assume that, if default occurs, the recovery at maturity depends on the ‘severity of default’. Under this general setting, the vehicle for our analysis is an integral equation. With the aid of this, we prove some properties of the bond price which are consistent numerically and empirically with earlier works. In particular, the limiting credit spread as time to maturity tends to 0 is nonzero. As a byproduct, we show that the integral equation implies an infinite-series expansion for the bond price.

Keywords

Jump diffusiondefault barrierbond pricecredit spread

MSC classification

Secondary: 60J25: Continuous-time Markov processes on general state spaces 60J75: Jump processes 60G44: Martingales with continuous parameter
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 1 , March 2009 , pp. 71 - 84
Copyright
Copyright © Applied Probability Trust 2009 

Footnotes

∗

Current address: Institute of Mathematics, Academia Sinica, Nankang, Taipei, Taiwan.

References

[1] Altman, E. I. and Bencivenga, J. C. (1995). A yield premium model for the high-yield debt market. Finanicial Analyst J. 51, 49–56.CrossRefGoogle Scholar
[2] Bingham, N. H. and Kiesel, R. (2004). Risk-Neutral Valuation, 2nd edn. Springer, London.Google Scholar
[3] Black, F. and Cox, J. C. (1976). Valuing corporate securities: some effects of bond indenture provisions. J. Finance 31, 351–367.Google Scholar
[4] Franks, J. R. and Torous, W. N. (1994). A comparison of financial recontracting in distressed exchanges and Chapter 11 organizations. J. Financial Econom. 35, 349–370.Google Scholar
[5] Hilberink, B. and Rogers, L. C. G. (2002). Optimal capital structure and endogenous default. Finance Stoch. 6, 237–363.Google Scholar
[6] Lando, D. (2004). Credit Risk Modeling. Princeton University Press.CrossRefGoogle Scholar
[7] Leland, H. E. (1994). Corporate debt value, bond covenants, and optimal capital structure. J. Finance 49, 1213–1252.CrossRefGoogle Scholar
[8] Longstaff, F. A. and Schwartz, E. S. (1995). A simple approach to valuing risky fixed and floating rate debt. J. Finance 50, 789–819.Google Scholar
[9] Merton, R. C. (1974). On the pricing of corporate debt: the risk structure of interest rates. J. Finance 29, 449–470.Google Scholar
[10] Shreve, S. E. (2004). Stochastic Calculus for Finance. II. Springer, New York.Google Scholar
[11] Zhou, C. (2001). The term structure of credit spreads with Jump risk. J. Banking Finance 26, 2015–2040.Google Scholar