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A jump-diffusion approach to modeling credit risk and valuing defaultable securities

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  • Chunsheng Zhou

Abstract

The existing structural models of credit risk have relied almost exclusively on diffusion processes to model the evolution of firm value. While a diffusion approach is convenient, it has produced very disappointing results in empirical application. Jones, Mason, and Rosenfeld (1984) find that the credit spreads on corporate bonds are too high to be matched by the diffusion approach. Also, because the instantaneous default probability of a healthy firm is zero under a continuous process, the diffusion approach predicts that the term structure of credit spreads should always start at zero and slope upward for firms that are not currently in financial distress. Empirical literature shows, however, that the actual credit spread curves are sometimes flat or even downward-sloping. If a diffusion approach cannot capture the basic features of credit risk, what approach can? This paper develops a new structural approach to valuing default-risky securities by modeling the evolution of firm value as a jump-diffusion process. Under a jump-diffusion process, a firm can default instantaneously because of a sudden drop in its value. With this characteristic, a jump-diffusion model can match the size of credit spreads on corporate bonds and can generate various shapes of yield spread curves and marginal default rate curves. The model also links recovery rates to firm value at default in a natural way so that variation in recovery rates is endogenously generated in the model. The model is also consistent with many other stylized empirical facts in the credit-risk literature.

Suggested Citation

  • Chunsheng Zhou, 1997. "A jump-diffusion approach to modeling credit risk and valuing defaultable securities," Finance and Economics Discussion Series 1997-15, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:1997-15
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    References listed on IDEAS

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    2. de Andrade, Fabio Wendling Muniz & Thomas, Lyn, 2007. "Structural models in consumer credit," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1569-1581, December.
    3. Albanese, Claudio & Chen, Oliver X., 2006. "Implied migration rates from credit barrier models," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 607-626, February.
    4. Ming Xi Huang, 2010. "Modelling Default Correlations in a Two-Firm Model with Dynamic Leverage Ratios," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 15, january-d.
    5. Elisa Luciano & Wim Schoutens, 2006. "A multivariate jump-driven financial asset model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 385-402.
    6. Bauerle, Nicole, 2002. "Risk management in credit risk portfolios with correlated assets," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 187-198, April.
    7. J.W. Nieuwenhuis & M.H. Vellekoop, 2004. "Weak convergence of tree methods, to price options on defaultable assets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(2), pages 87-107, December.
    8. Georges Dionne & Sadok Laajimi & Sofiane Mejri & Madalina Petrescu, 2006. "Estimation of the Default Risk of Publicly Traded Canadian Companies," Cahiers de recherche 0613, CIRPEE.
    9. repec:wsi:ijtafx:v:06:y:2003:i:06:n:s0219024903002158 is not listed on IDEAS
    10. repec:spr:joptap:v:157:y:2013:i:1:d:10.1007_s10957-012-0138-y is not listed on IDEAS
    11. Trueck, Stefan & Rachev, Svetlozar T., 2008. "Rating Based Modeling of Credit Risk," Elsevier Monographs, Elsevier, edition 1, number 9780123736833.
    12. Chiarella, Carl & Fanelli, Viviana & Musti, Silvana, 2011. "Modelling the evolution of credit spreads using the Cox process within the HJM framework: A CDS option pricing model," European Journal of Operational Research, Elsevier, vol. 208(2), pages 95-108, January.
    13. Becchetti, Leonardo & Carpentieri, Andrea & Hasan, Iftekhar, 2009. "The determinants of option-adjusted delta credit spreads : a comparative analysis of the United States, the United Kingdom and the euro area," Research Discussion Papers 34/2009, Bank of Finland.
    14. Luis H. R. Alvarez & Jani Sainio, 2010. "A Loan Portfolio Model Subject to Random Liabilities and Systemic Jump Risk," Papers 1006.0863, arXiv.org.
    15. repec:gam:jrisks:v:5:y:2017:i:4:p:65-:d:123567 is not listed on IDEAS
    16. Rocha, Katia & Alcaraz Garcia, Francisco Augusto & Teixeira, José Paulo, 2007. "Term Structure of Sovereign Spreads - A Contingent Claim Model," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 61(4), July.
    17. Campi, Luciano & Polbennikov, Simon & Sbuelz, Alessandro, 2009. "Systematic equity-based credit risk: A CEV model with jump to default," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 93-108, January.
    18. Stuart M. Turnbull & Jun Yang, 2004. "Modelling the Evolution of Credit Spreads in the United States," Staff Working Papers 04-45, Bank of Canada.
    19. Maclachlan, Iain C, 2007. "An empirical study of corporate bond pricing with unobserved capital structure dynamics," MPRA Paper 28416, University Library of Munich, Germany.
    20. Lotz, Christopher & Schlogl, Lutz, 2000. "Default risk in a market model," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 301-327, January.
    21. Allen, Linda & DeLong, Gayle & Saunders, Anthony, 2004. "Issues in the credit risk modeling of retail markets," Journal of Banking & Finance, Elsevier, vol. 28(4), pages 727-752, April.

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