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A Regime Switching Model for the Term Structure of Credit Risk Spreads
Department of Finance, University of Nevada Las Vegas, Las Vegas, NV, USA
Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV, USA
- 1 Department of Finance, University of Nevada Las Vegas, Las Vegas, NV, USA
- 2 Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV, USA
Journal of Mathematical Finance·Volume 05 (2015)·Pages 49–57·Published 20 January 2015·DOI10.4236/jmf.2015.51005
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Abstract
We consider a rating-based model for the term structure of credit risk spreads wherein the credit-worthiness of the issuer is represented as a finite-state continuous time Markov process. This approach entails a progressive drift in credit quality towards default. A model of the economy is presented featuring stochastic transition probabilities; credit instruments are valued via an ultra parabolic Hamilton-Jacobi system of equations discretized utilizing the method-of-lines finite difference method. Computations for a callable bond are presented demonstrating the efficiency of the method.
KeywordsOptimal StoppingFailure RateRegime SwitchingCredit Risk Spreads
- Bielicki, T. and Rutkowski, M. (2002) Credit Risk: Modeling, Valuation and Hedging. Springer-Verlag, Berlin.
- Lando, D. (1998) On Cox Processes and Credit Risky Securities. Review of Derivative Research, 2, 99-120. http://dx.doi.org/10.1007/BF01531332
- Duffie, D. and Singleton, K. (1999) Modeling Term Structures of Defaultable Bonds. Review of Financial Studies, 12, 687-720. http://dx.doi.org/10.1007/BF01531332
- Longstaff, F. and Schwartz, E. (1995) Valuing Credit Derivatives. The Journal of Fixed Income, 5, 6-12. http://dx.doi.org/10.3905/jfi.1995.408138
- Jobst, N. and Zenios, S.A. (2005) On the Simulation of Interest Rate and Credit Risk Sensitive Securities. European Journal of Operational Research, 161, 298-324. http://dx.doi.org/10.1016/j.ejor.2003.08.044
- Jarrow, R., Lando, D. and Turnbull, S. (1997) A Markov Model for the Term Structure of Credit Risk Spreads. Review of Financial Studies, 10, 481-523. http://dx.doi.org/10.1093/rfs/10.2.481
- Das, S. and Tufano, P. (1996) Pricing Credit Sensitive Debt When Interest Rates, Credit Ratings and Credit Spreads Are Stochastic. Journal of Financial Engineering, 5, 161-198.
- Arvantis, A., Gregory, J. and Laurent, J.-P. (1999) Building Models for Credit Spreads. The Journal of Derivatives, 6, 27-43.
- Elliott, R.J. and Mamon R.S. (2002) An Interest Rate Model with a Markovian Mean Reverting Level. Quantitative Finance, 2, 454-458. http://dx.doi.org/10.1080/14697688.2002.0000012
- Wu, S. and Zeng, Y. (2005) A General Equilibrium Model of the Term Structure of Interest Rates under Regime-Switching Risk. International Journal of Theoretical and Applied Finance, 8, 1-31.
- Harrison, J.M. and Pliska, S. (1981) Martingales and Stochastic Integrals in the Theory of Continuous Trading. Stochastic Processes and Their Applications, 11, 215-260. http://dx.doi.org/10.1016/0304-4149(81)90026-0
- Jarrow, R. and Turnbull, S. (1995) Pricing Derivatives on Financial Securities Subject to Credit Risk. Journal of Finance, 50, 53-85. http://dx.doi.org/10.1111/j.1540-6261.1995.tb05167.x
- Karlin, S. and Taylor, H. (1975) A First Course in Stochastic Processes. Academic Press, New York.
- Elliott, R.J., Aggoun, L. and Moore, J.B. (1994) Hidden Markov Models: Estimation and Control. Springer-Verlag, New York.