Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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DEFAULTABLE BOND PRICING USING REGIME SWITCHING INTENSITY MODEL

  • Goutte, Stephane (Laboratoire de Probabilites et Modeles Aleatoires (LPMA), Universite Paris Diderot) ;
  • Ngoupeyou, Armand (Laboratoire de Probabilites et Modeles Aleatoires (LPMA), Universite Paris Diderot)
  • Received : 2012.06.22
  • Accepted : 2012.12.05
  • Published : 2013.09.30
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Abstract

In this paper, we are interested in finding explicit numerical formulas to evaluate defaultable bonds prices of firms. For this purpose, we use a default intensity whose values depend on the credit rating of these firms. Each credit rating corresponds to a state of the default intensity. Then, this regime switches as soon as one of the credit rating of a firm also changes. Moreover, this regime switching default intensity model allows us to capture well some market features or economics behaviors. Thus, we obtain two explicit different formulas to evaluate the conditional Laplace transform of a regime switching Cox Ingersoll Ross model. One using the property of semi-affine of the model and the other one using analytic approximation. We conclude by giving some numerical illustrations of these formulas and real data estimation results.

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References

  1. A. Alfonsi and D. Brigo, Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model, Finance Stochastic 9 (2005), 29-42. https://doi.org/10.1007/s00780-004-0131-x
  2. T. R. Bielecki, J. Jakubowski, A. Vidozzi and L. Vidozzi, Study of dependence for some stochastic processes, Stoch. Anal. Appl. 26 no. 4 (2008), 903-924. https://doi.org/10.1080/07362990802128958
  3. T. R. Bielecki, M. Jeanblanc and M. Rutkowski, Credit risk, Lecture Note of Lisbonn. http://www.maths.univ-evry.fr/pagesperso/jeanblanc/conferences/lisbon.pdf. (2006)
  4. T.R. Bielecki and M. Rutkowski, Credit Risk: Modeling, Valuation and Hedging, Springer 2002.
  5. S. Choi, Regime-Switching Univariate Diffusion Models of the Short-Term Interest Rate, Studies in Nonlinear Dynamics & Econometrics, 13, No. 1, Article 4 (2009).
  6. Y. Choi and T.S. Wirjanto, An analytic approximation formula for pricing zero-coupon bonds, Finance Research Letters, 4, (2007), 116-126. https://doi.org/10.1016/j.frl.2007.02.001
  7. J.C. Cox, J. Ingersoll and S. Ross, A theory of the term structure of interest rates, Econometrica, 53 (1985), 385-405. https://doi.org/10.2307/1911242
  8. D. Duffie, D. Filipovic and W. Schachermayer, Affine processes and applications in finance, Ann. Appl. Probab. 13, Number 3, (2003) 984-1053. https://doi.org/10.1214/aoap/1060202833
  9. D. Duffie and K. Singleton, Credit risk: Pricing, Measurement and Management, Princeton University Press, Princeton 2003.
  10. E. Eberlein and F. Ozkan, The defaultable Levy term structure: ratings and restructuring, Mathematical Finance 13 (2003), 277-300. https://doi.org/10.1111/1467-9965.00017
  11. R.J. Elliott, L. Aggoun and J.B. Moore, Hidden Markov Models: Estimation and Control, Springer-Verlag, New York 1995.
  12. N. El Karoui, M. Jeanblanc and Y. Jiao, What happens after a default: the conditionnal density approach, Preprint (2009).
  13. Z. Grbac, Credit Risk in Levy Libor Modeling: Rating Based Approach, Dissertation. University Freibourg. http://www.freidok.uni-freiburg.de/volltexte/7253/pdf/diss.pdf (2009).
  14. C. Gourieroux, Continuous time Wishart process for stochastic risk, Econometric Reviews, 25 (2-3) (2006),177-217. https://doi.org/10.1080/07474930600713234
  15. S. Goutte and B. Zou, Continuous time regime switching model applied to foreign exchange rate, Preprint (2012).
  16. J. Hamilton, Rational-expectations econometric analysis of changes in regime, Journal of Economic Dynamics and Control, 12 (1989), 385-423.
  17. J.M. Harrison and S.R. Pliska, Martingales and stochastic integrals in the theory of continuous trading, Stoch. Proces. Appl. 11 (1981), 381-408.
  18. J.M. Harrison and S.R. Pliska, A stochastic calculus model of continuous time trading: complete markets, Stoch. Proces. Appl. 13 (1983), 313-316.
  19. S. Heston, A closed-Form Solution for Options with Stochastic Volatility with Application to Bond and Currency Options, Review of Financial Studies, 6 (1993), 327-343. https://doi.org/10.1093/rfs/6.2.327
  20. M. Jeanblanc and M. Rutkowski, Mathematical Finance-Bachelier Congress 2000, Chapter Default risk and hazard process , 281-312, Springer-Verlag Berlin 2002.
  21. D. Lando, On Cox Processes and Credit Risky Securities, Review of Derivatives Research, 2 (1998), 99-120.
  22. D. Madan and H. Unal, Pricing the risks of default, Review of Derivatives Research 2 (1998), 121-160.
  23. R. Merton, On the pricing of corporate debt: the risk structure of interest rates, J. of Finance, 3 (1974), 449-470.

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