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Valuing risky debt: A new model combining structural information with the reduced-form approach

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  • Ballestra, Luca Vincenzo
  • Pacelli, Graziella

Abstract

A new model of credit risk is proposed in which the intensity of default is described by an additional stochastic differential equation coupled with the process of the obligor’s asset value. Such an approach allows us to incorporate structural information as well as to capture the effect of external factors (e.g. macroeconomic factors) in a both parsimonious and economically consistent way. From the practical standpoint, the proposed model offers great flexibility and allows us to obtain credit spread curves of many different shapes, including double humped term structures. Furthermore, an approximate closed-form solution is derived, which is accurate, easy to implement, and allows for an efficient calibration to realized credit spreads. Numerical experiments are presented showing that the novel approach provides a very satisfactory fitting to market data and outperforms the model developed by Madan and Unal (2000).

Suggested Citation

  • Ballestra, Luca Vincenzo & Pacelli, Graziella, 2014. "Valuing risky debt: A new model combining structural information with the reduced-form approach," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 261-271.
    • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:261-271
    DOI: 10.1016/j.insmatheco.2014.02.002
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    1. Briys, Eric & de Varenne, François, 1997. "Valuing Risky Fixed Rate Debt: An Extension," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(2), pages 239-248, June.
    2. Duffee, Gregory R, 1999. "Estimating the Price of Default Risk," The Review of Financial Studies, Society for Financial Studies, vol. 12(1), pages 197-226.
    3. Jones, E Philip & Mason, Scott P & Rosenfeld, Eric, 1984. "Contingent Claims Analysis of Corporate Capital Structures: An Empirical Investigation," Journal of Finance, American Finance Association, vol. 39(3), pages 611-625, July.
    4. Kamhon Kan, 1998. "Credit spreads on government bonds," Applied Financial Economics, Taylor & Francis Journals, vol. 8(3), pages 301-313.
    5. Frank Fabozzi & Yi-Chen Wang & Shih-Kuo Yeh & Ren-Raw Chen, 2009. "An empirical analysis of the CDX index and its tranches," Applied Economics Letters, Taylor & Francis Journals, vol. 16(14), pages 1425-1431.
    6. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    7. Liang, Xue & Wang, Guojing, 2012. "On a reduced form credit risk model with common shock and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 567-575.
    8. Houweling, Patrick & Hoek, Jaap & Kleibergen, Frank, 2001. "The joint estimation of term structures and credit spreads," Journal of Empirical Finance, Elsevier, vol. 8(3), pages 297-323, July.
    9. Chen, Cho-Jieh & Panjer, Harry, 2003. "Unifying discrete structural models and reduced-form models in credit risk using a jump-diffusion process," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 357-380, October.
    10. Abínzano, Isabel & Seco, Luis & Escobar, Marcos & Olivares, Pablo, 2009. "Single and Double Black-Cox: Two approaches for modelling debt restructuring," Economic Modelling, Elsevier, vol. 26(5), pages 910-917, September.
    11. Madan, Dilip & Unal, Haluk, 2000. "A Two-Factor Hazard Rate Model for Pricing Risky Debt and the Term Structure of Credit Spreads," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 35(1), pages 43-65, March.
    12. George Athanassakos & Peter Carayannopoulos, 2001. "An empirical analysis of the relationship of bond yield spreads and macro economic factors," Applied Financial Economics, Taylor & Francis Journals, vol. 11(2), pages 197-207.
    13. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    14. David Beckworth & Kenneth Moon & J. Holland Toles, 2010. "Monetary policy and corporate bond yield spreads," Applied Economics Letters, Taylor & Francis Journals, vol. 17(12), pages 1139-1144.
    15. Leland, Hayne E & Toft, Klaus Bjerre, 1996. "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    16. Bauerle, Nicole, 2002. "Risk management in credit risk portfolios with correlated assets," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 187-198, April.
    17. Longstaff, Francis A & Schwartz, Eduardo S, 1995. "A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    18. Yi-Hsuan Chen & Kehluh Wang & Anthony Tu, 2011. "Default correlation at the sovereign level: evidence from some Latin American markets," Applied Economics, Taylor & Francis Journals, vol. 43(11), pages 1399-1411.
    19. Christopher Baum & Chi Wan, 2010. "Macroeconomic uncertainty and credit default swap spreads," Applied Financial Economics, Taylor & Francis Journals, vol. 20(15), pages 1163-1171.
    20. Luca Vincenzo Ballestra & Graziella Pacelli, 2009. "A Numerical Method to Price Defaultable Bonds Based on the Madan and Unal Credit Risk Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 17-36.
    21. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    22. Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, Francois, 2005. "Market value of life insurance contracts under stochastic interest rates and default risk," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 499-516, June.
    23. de Wet, Albertus H. & van Eyden, Reneé & Gupta, Rangan, 2009. "Linking global economic dynamics to a South African-specific credit risk correlation model," Economic Modelling, Elsevier, vol. 26(5), pages 1000-1011, September.
    24. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    25. Feng, Runhuan & Volkmer, Hans W., 2012. "Modeling credit value adjustment with downgrade-triggered termination clause using a ruin theoretic approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 409-421.
    26. D. P. Gaver, 1966. "Observing Stochastic Processes, and Approximate Transform Inversion," Operations Research, INFORMS, vol. 14(3), pages 444-459, June.
    27. Pierre Collin‐Dufresne & Robert S. Goldstein, 2001. "Do Credit Spreads Reflect Stationary Leverage Ratios?," Journal of Finance, American Finance Association, vol. 56(5), pages 1929-1957, October.
    28. Lara Cathcart & Lina El-Jahel, 2006. "Pricing defaultable bonds: a middle-way approach between structural and reduced-form models," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 243-253.
    29. Anderson, Ronald W & Sundaresan, Suresh, 1996. "Design and Valuation of Debt Contracts," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 37-68.
    30. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    31. repec:bla:jfinan:v:44:y:1989:i:5:p:1351-60 is not listed on IDEAS
    32. Zhou, Chunsheng, 2001. "The term structure of credit spreads with jump risk," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 2015-2040, November.
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    2. Hyong-Chol O. & Jong-Chol Kim & Il-Gwang Jon, 2017. "Numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon," Papers 1709.06517, arXiv.org, revised Aug 2018.
    3. Hyong Chol O & Tae Song Kim, 2020. "Analysis on the Pricing model for a Discrete Coupon Bond with Early redemption provision by the Structural Approach," Papers 2007.01511, arXiv.org.
    4. Hainaut, Donatien, 2020. "Credit risk modelling with fractional self-excited processes," LIDAM Discussion Papers ISBA 2020002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Qiu, Ming & Jin, Zhuo & Li, Shuanming, 2023. "Optimal risk sharing and dividend strategies under default contagion: A semi-analytical approach," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 1-23.
    6. Hainaut, Donatien, 2019. "Credit risk modelling with fractional self-excited processes," LIDAM Discussion Papers ISBA 2019027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Liu, Jing, 2018. "LLN-type approximations for large portfolio losses," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 71-77.
    8. Cantia, Catalin & Tunaru, Radu, 2017. "A factor model for joint default probabilities. Pricing of CDS, index swaps and index tranches," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 21-35.
    9. Feng-Hui Yu & Jiejun Lu & Jia-Wen Gu & Wai-Ki Ching, 2019. "Modeling Credit Risk with Hidden Markov Default Intensity," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 1213-1229, October.

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