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Journal of Applied Mathematics
Volume 2013, Article ID 138272, 12 pages
Research Article

Structural Credit Risk Models with Subordinated Processes

1Department of Management, Economics and Quantitative Methods, University of Bergamo, Via dei Caniana 2, 24127 Bergamo, Italy
2Department of Applied Finance and Actuarial Studies, Macquarie University, Eastern Road, North Ryde, NSW 2109, Australia
3Department of Finance, Faculty of Economics, VŠB-Technical University of Ostrava, Sokolská 33, 70121 Ostrava, Czech Republic

Received 31 January 2013; Accepted 15 July 2013

Academic Editor: Xiaoning Zhang

Copyright © 2013 Martin Gurny et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. C. Merton, “On the pricing of corporate debt: the risk structure of interest rates,” Journal of Finance, vol. 29, pp. 449–470, 1974. View at Google Scholar
  2. F. Black and M. Scholes, “The pricing of options and corporate liabilities,” Journal of Political Economy, vol. 81, pp. 637–659, 1973. View at Google Scholar
  3. C. Bluhm, L. Overbeck, and C. Wagner, An Introduction to Credit Risk Modeling, CRC Press, Boca Raton, Fla, USA, 1st edition, 2003.
  4. D. Duffie and K. J. Singleton, Credit Risk: Pricing, Measurement, and Management, Princeton University Press, Princeton, NJ, USA, 1st edition, 2003.
  5. P. J. Crosbie and J. R. Bohn, “Modelling default risk,” Working Paper, KMV Corporation, 2003. View at Google Scholar
  6. J. R. Bohn, N. Arora, and I. Korablev, “Power and level validation of the EDF credit measure in the U.S. market,” Moody’s KMV Working Paper, 2005. View at Google Scholar
  7. Y. Du and W. Suo, “Assessing credit quality from equity markets: is structural model a better approach,” Working Paper, Queen’s University, 2003. View at Google Scholar
  8. S. A. Hillegeist, E. K. Keating, D. P. Cram, and K. G. Lundstedt, “Assessing the probability of Bankruptcy,” Working Paper, Kellog School of Management, 2002. View at Google Scholar
  9. D. Duffie, L. Saita, and K. Wang, “Multi-period corporate default prediction with stochastic covariates,” Journal of Financial Economics, vol. 83, no. 3, pp. 635–665, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. E. S. Farmen, S. Westgaard, S. Fleten, and N. Wijst, “Default risk and its Greeks under an objective probability measure,” in Proceedings of the Stockholm School of Economics—Department of Finance Seminar Series, November 2003.
  11. F. Black and C. Cox, “Valuing corporate securities: some effects of bond indenture provisions,” Journal of Finance, vol. 31, no. 2, pp. 351–367, 1976. View at Google Scholar
  12. J. R. Bohn, “A survey of contingent-claims approaches to risky debt valuation,” The Journal of Risk Finance, vol. 1, no. 3, pp. 53–70, 2000. View at Publisher · View at Google Scholar
  13. J. C. Duan, “Maximum likelihood estimation using price data of the derivative contract,” Mathematical Finance, vol. 4, no. 2, pp. 155–157, 1994. View at Google Scholar
  14. B. Mandelbrot, “New methods in statistical economics,” Journal of Political Economy, vol. 71, pp. 421–440, 1963. View at Google Scholar
  15. B. Mandelbrot, “The variation of certain speculative prices,” Journal of Business, vol. 26, pp. 394–419, 1963. View at Google Scholar
  16. B. Mandelbrot, “The variation of some other speculative prices,” Journal of Business, vol. 40, pp. 393–413, 1967. View at Google Scholar
  17. E. Fama, “Mandelbrot and the stable Paretian hypothesis,” Journal of Business, vol. 36, pp. 420–429, 1963. View at Google Scholar
  18. E. Fama, “The behavior of stock market prices,” Journal of Business, vol. 38, pp. 34–105, 1965. View at Google Scholar
  19. E. Fama, “Portfolio analysis in a stable Paretian market,” Management Science, vol. 11, pp. 404–419, 1965. View at Google Scholar
  20. S. Rachev and S. Mittnik, Stable Paretian Model in Finance, John Wiley & Sons, Chichester, UK, 2000.
  21. S. R. Hurst, E. Platen, and S. T. Rachev, “Option pricing for a logstable asset price model,” Mathematical and Computer Modelling, vol. 29, no. 10–12, pp. 105–119, 1999. View at Publisher · View at Google Scholar · View at Scopus
  22. T. Mandelbrot and M. Taylor, “On the distribution of stock price differences,” Operations Research, vol. 15, pp. 1057–1062, 1967. View at Google Scholar
  23. S. T. Rachev, Handbook of Heavy Tailed Distributions in Finance, Elsevier, Amsterdam, The Netherlands, 2003.
  24. G. Deliandes and R. Geske, “Credit risk and risk neutral default probabilities—information about rating migrations and defaults,” Working Paper, UCLA, 2003. View at Google Scholar
  25. M. F. Osborne, “Brownian motion in the stock market,” Operations Research, vol. 7, pp. 145–173, 1959. View at Google Scholar
  26. W. Feller, An Introduction to Probability Theory and Its Applications II, John Wiley & Sons, New York, NY, USA, 1966.
  27. N. Hofmann, E. Platen, and M. Schweizer, “Option pricing under incompleteness and stochastic volatility,” Tech. Rep., Department of Mathematics, University of Bonn, 1982. View at Google Scholar
  28. H. Follmer and D. Sondermann, “Hedging of non-redundant contingent claims,” in Contributions to Mathematical Economics, W. Hildenbrand and A. M. Aollell, Eds., pp. 205–223, North-Holland, Amsterdam, The Netherlands, 1986. View at Google Scholar
  29. H. Follmer and M. Schweizer, “Microeconomic approach to diffusion models for stock prices,” Mathematical Finance, vol. 3, pp. 1–23, 1989. View at Google Scholar
  30. G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman & Hall, New York, NY, USA, 1994.
  31. M. Bruche, “Estimating structural bond pricing models via simulated maximum likelihood,” 2005,
  32. J. Ericsson and J. Reneby, “Estimating structural bond pricing models,” Journal of Business, vol. 78, no. 2, pp. 707–736, 2005. View at Publisher · View at Google Scholar · View at Scopus
  33. M. Jovan, “The Merton structural model and IRB compliance,” Metodološki Zvezki, vol. 7, no. 1, pp. 39–57, 2010. View at Google Scholar
  34. J. C. Duan, G. Gauthier, and J. G. Simonato, “On the equivalence of the KMV and maximum likelihood methods for structural credit risk models,” 2004,
  35. M. Vassalou and Y. Xing, “Default risk in equity returns,” Journal of Finance, vol. 59, no. 2, pp. 831–868, 2004. View at Publisher · View at Google Scholar · View at Scopus
  36. N. Arora, J. R. Bohn, and F. Zhu, “Reduced form versus structural models of credit risk: a case study of three models,” Moody’s KMV Working Paper, 2005. View at Google Scholar
  37. S. T. Bharath and T. Shumway, “Forecasting default with the Merton distance to default model,” Review of Financial Studies, vol. 21, no. 3, pp. 1339–1369, 2008. View at Publisher · View at Google Scholar · View at Scopus
  38. C. M. Jarque and A. K. Bera, “A test for normality of observations and regression residuals,” International Statistical Review, vol. 55, no. 2, pp. 163–172, 1987. View at Google Scholar
  39. H. N. Byström, “Merton for dummies: a flexible way of modelling default risk,” Research Paper 112, University of Technology, Sydney, Australia, 2003. View at Google Scholar
  40. J. P. Nolan, “Numerical calculation of stable densities and distribution functions,” Communications in Statistics C, vol. 13, no. 4, pp. 759–774, 1997. View at Google Scholar · View at Scopus