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Free boundaries of credit rating migration in switching macro regions

  • * Corresponding author: Jin Liang

    * Corresponding author: Jin Liang

The second author is supported by National Natural Science Foundation of China (No. 11671301)

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  • In this paper, under the structure framework, a valuation model for a corporate bond with credit rating migration risk and in macro regime switch is established. The model turns to a free boundary problem in a partial differential equation (PDE) system. By PDE techniques, the existence, uniqueness and regularity of the solution are obtained. Furthermore, numerical examples are also presented.

    Mathematics Subject Classification: Primary: 35R35, 35K40; Secondary: 35Q91.

    Citation:

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  • Figure 1.  Value function in different regimes

    Figure 2.  Free boundary

    Figure 3.  Differences between two cases

  • [1] F. Black and J. C. Cox, Some effects of bond indenture provisions, Journal of Finance, 31 (1976), 351-367. 
    [2] N. P. B. Bollen, Valuing options in regime-switching models, Journal of Derivatives, 6 (1998), 38-49.  doi: 10.3905/jod.1998.408011.
    [3] L. CholleteA. Heinen and A. Valdesogo, Modeling international financial returns with a multivariate regime switching copula, Journal of Financial Econometrics, 7 (2008), 437-480. 
    [4] S. Das and P. Tufano, Pricing credit-sensitive debt when interest rates, credit ratings, and credit spreads are stochastic, Journal of Financial Engineering, 5 (1996), 161-198. 
    [5] F. X. Diebold, J. Lee and G. C. Weinbach, Regime switching with time-varying transition probabilities, in Nonstationary Time Series Analysis and Cointegration (ed. C. Hargreaves), Oxford University Press, (1993), 283–302.
    [6] D. Duffe and K. J. Singleton, Modeling term structures of defaultable bonds, The Review of Financial Studies, 12 (1999), 687-720.  doi: 10.1093/rfs/12.4.687.
    [7] J. D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica, 57 (1989), 357-384.  doi: 10.2307/1912559.
    [8] M. R. Hardy, A regime-switching model of long-term stock returns, North American Actuarial Journal, 5 (2001), 41-53.  doi: 10.1080/10920277.2001.10595984.
    [9] B. Hu, Blow-up Theories for Semilinear Parabolic Equations, Springer, Heidelberg, New York, 2011. doi: 10.1007/978-3-642-18460-4.
    [10] B. HuJ. Liang and Y. Wu, A free boundary problem for corporate bond with credit rating migration, Journal of Mathematical Analysis and Applications, 428 (2015), 896-909.  doi: 10.1016/j.jmaa.2015.03.040.
    [11] R. A. Jarrow and S. M. Turnbull, Pricing derivatives on financial securities subject to credit risk, Financial Derivatives Pricing, (2008), 377–409. doi: 10.1142/9789812819222_0017.
    [12] R. JarrowD. Lando and S. Turnbull, A Markov model for the term structure of credit risk spreads, Review of Financial studies, 10 (1997), 481-523. 
    [13] L. S. Jiang, Mathematical Modeling and Methods for Option Pricing, World Scientific Publishing Co., Inc., River Edge, NJ, 2005. doi: 10.1142/5855.
    [14] D. Lando, On cox processes and credit-risky securities, Review of Derivatives Research, 2 (1998), 99-120. 
    [15] H. Leland and B.K. Toft, Optimal capital structure, endogenous bankruptcy, and the term structure of credit spreads, Journal of Finance, 51 (1996), 987-1019. 
    [16] J. LiangY. Wu and B. Hu, Asymptotic traveling wave solution for a credit rating migration problem, Journal of Differential Equations, 261 (2016), 1017-1045.  doi: 10.1016/j.jde.2016.03.032.
    [17] J. Liang and C. K. Zeng, Corporate bonds pricing under credit rating migration and structure framework, Applied Mathematics A Journal of Chinese Universities, 30 (2015), 61-70. 
    [18] J. LiangY. J. Zhao and X. D. Zhang, Utility indifference valuation of corporate bond with credit rating migration by structure approach, Economic Modelling, 54 (2016), 339-346.  doi: 10.1016/j.econmod.2015.12.002.
    [19] R. C. Merton, On the pricing of corporate debt: The risk structure of interest rates, Journal of Finance, 29 (1974), 449-470.  doi: 10.1142/9789814759588_0003.
    [20] L. ThomasD. Allen and N. Morkel-Kingsbury, A hidden Markov chain model for the term structure of bond credit risk spreads, International Review of Financial Analysis, 11 (2002), 311-329. 
    [21] W. Weron, Modelling electricity prices: Jump diffusion and regime switching, Physica A Statistical Mechanics and Its Applications, 336 (2004), 39-48. 
    [22] Y. Wu and J. Liang, A new model and its numerical method to identify multi credit migration boundaries, International Journal of Computer Mathematics, 95 (2018), 1688-1702.  doi: 10.1080/00207160.2017.1329529.
    [23] Q. YeZ. LiM. Wang and  Y. WuIntroduction of Reaction-Defusion Equation, 2 edition, Science Press, Beijing, 2011. 
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