A Regime Switching Model for the Term Structure of Credit Risk Spreads

Seungmook Choi¹, Michael D. Marcozzi²

¹Department of Finance, University of Nevada Las Vegas, Las Vegas, NV, USA.
²Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV, USA.

DOI: 10.4236/jmf.2015.51005                

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.

Keywords

Optimal Stopping, Failure Rate, Regime Switching, Credit Risk Spreads

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Bielicki, T. and Rutkowski, M. (2002) Credit Risk: Modeling, Valuation and Hedging. Springer-Verlag, Berlin.
[2]	Lando, D. (1998) On Cox Processes and Credit Risky Securities. Review of Derivative Research, 2, 99-120. http://dx.doi.org/10.1007/BF01531332
[3]	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
[4]	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
[5]	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
[6]	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
[7]	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.
[8]	Arvantis, A., Gregory, J. and Laurent, J.-P. (1999) Building Models for Credit Spreads. The Journal of Derivatives, 6, 27-43.
[9]	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
[10]	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.
[11]	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
[12]	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
[13]	Karlin, S. and Taylor, H. (1975) A First Course in Stochastic Processes. Academic Press, New York.
[14]	Elliott, R.J., Aggoun, L. and Moore, J.B. (1994) Hidden Markov Models: Estimation and Control. Springer-Verlag, New York.
[15]	Brémaud, P. (1998) Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues. Springer-Verlag, New York.
[16]	Marcozzi, M.D. (2001) On the Approximation of Optimal Stopping Problems with Application to Financial Mathematics. SIAM Journal on Scientific Computing, 22, 1865-1884. http://dx.doi.org/10.1137/S1064827599364647
[17]	Marcozzi, M.D. (2015) Optimal Control of Ultradiffusion Processes with Application to Mathematical Finance. International Journal of Computer Mathematics, 92, 296-318. http://dx.doi.org/10.1080/00207160.2014.890714