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

  • Chunsheng Zhou

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.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 1997-15.

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Date of creation: 1997
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Handle: RePEc:fip:fedgfe:1997-15
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  1. Altman, Edward I, 1989. " Measuring Corporate Bond Mortality and Performance," Journal of Finance, American Finance Association, vol. 44(4), pages 909-22, September.
  2. Duffee, Gregory R., 1996. "On measuring credit risks of derivative instruments," Journal of Banking & Finance, Elsevier, vol. 20(5), pages 805-833, June.
  3. Merton, Robert C., 1977. "On the pricing of contingent claims and the Modigliani-Miller theorem," Journal of Financial Economics, Elsevier, vol. 5(2), pages 241-249, November.
  4. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  5. Jarrow, Robert A & Lando, David & Turnbull, Stuart M, 1997. "A Markov Model for the Term Structure of Credit Risk Spreads," Review of Financial Studies, Society for Financial Studies, vol. 10(2), pages 481-523.
  6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  7. Kon, Stanley J, 1984. " Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-65, March.
  8. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
  9. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 541-552, November.
  10. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
  11. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  12. Jarrow, Robert A & Rosenfeld, Eric R, 1984. "Jump Risks and the Intertemporal Capital Asset Pricing Model," The Journal of Business, University of Chicago Press, vol. 57(3), pages 337-51, July.
  13. Chance, Don M, 1990. " Default Risk and the Duration of Zero Coupon Bonds," Journal of Finance, American Finance Association, vol. 45(1), pages 265-74, March.
  14. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
  15. Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, vol. 50(1), pages 53-85, March.
  16. Weiss, Lawrence A., 1990. "Bankruptcy resolution: Direct costs and violation of priority of claims," Journal of Financial Economics, Elsevier, vol. 27(2), pages 285-314, October.
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