### Quantitative Finance and Economics

2017, Issue 3: 300-319. doi: 10.3934/QFE.2017.3.300
Research article Special Issues

# On a Corporate Bond Pricing Model with Credit Rating Migration Risksand Stochastic Interest Rate

• Received: 27 July 2017 Accepted: 26 September 2017 Published: 12 October 2017
• In this paper we study a corporate bond-pricing model with credit rating migration and a stochastic interest rate. The volatility of bond price in the model strongly depends on potential credit rating migration and stochastic change of the interest rate. This new model improves the previous existing models in which the interest rate is considered to be a constant. The existence, uniqueness and regularity of the solution for the model are established. Moreover, some properties including the smoothness of the free boundary are obtained. Furthermore, some numerical computations are presented to illustrate the theoretical results.

Citation: Jin Liang, Hong-Ming Yin, Xinfu Chen, Yuan Wu. On a Corporate Bond Pricing Model with Credit Rating Migration Risksand Stochastic Interest Rate[J]. Quantitative Finance and Economics, 2017, 1(3): 300-319. doi: 10.3934/QFE.2017.3.300

### Related Papers:

• In this paper we study a corporate bond-pricing model with credit rating migration and a stochastic interest rate. The volatility of bond price in the model strongly depends on potential credit rating migration and stochastic change of the interest rate. This new model improves the previous existing models in which the interest rate is considered to be a constant. The existence, uniqueness and regularity of the solution for the model are established. Moreover, some properties including the smoothness of the free boundary are obtained. Furthermore, some numerical computations are presented to illustrate the theoretical results.

 [1] Black F, Cox JC (1976) Some Effects of Bond Indenture Provisions. J Financ 31: 351-367. doi: 10.1111/j.1540-6261.1976.tb01891.x [2] Briys E, Varenne DF (1997) Valuing Risky Fixed Rate Debt: An Extension. J Financ Quantit Anal 32: 239-249. doi: 10.2307/2331175 [3] Duffe D, Singleton KJ (1999) Modeling Term Structures of Defaultable Bonds. Rev Financ Stud 12: 687-720. doi: 10.1093/rfs/12.4.687 [4] Das S, Tufano P (1996) Pricing credit-sensitive debt when interest rates, credit ratings, and credit spreads are stochastic. J Financ Eng 5: 161-198. [5] Dixit AK, Pindyck S (1994) Investment under Uncertainty, Princeton Univ Press. [6] Evans LC (1978) A free boundary problem: the flow of two immiscible fluids in a one-dimensional porous medium. II. Indiana Univ Math J 27: 93-101. doi: 10.1512/iumj.1978.27.27009 [7] Friedman A (1982) Variational Principles and Free Boundary Problems. John Wiley Sons, New York. [8] Garrori MG; Menaldi JL (1992) Green Functions for Second Order Parabolic Integro-differential Problems. Longman Sci Tech, New York. [9] Hall J (1989) Options, Futures, and Other Derivatives, Prentice-Hall. Inc, New Jersey. [10] Hu B (2011) Blow-up Theories for Semilinear Parabolic Equations, Heidelberg ; New York : Springer. [11] Jiang L (2005) Mathematical Modeling and Methods for Option Pricing. World Sci. [12] Hu B, Liang J, Wu Y (2015) A Free Boundary Problem for Corporate Bond with Credit Rating Migration. J Math Anal Appl 428: 896-909. doi: 10.1016/j.jmaa.2015.03.040 [13] Hurd T, Kuznetsov A (2007) Affine Markov chain models of multifirm credit migration. J Credit Risk 3: 3-29. [14] Jarrow R, Turnbull S (1995) Pricing Derivatives on Financial Securities Subject to Credit Risk. J Financ 50: 53-86. doi: 10.1111/j.1540-6261.1995.tb05167.x [15] Jarrow RA, Lando D, TurnbullS M (1997) A Markov model for the term structure of credit risk spreads. Rev Financ stud 10: 481-523. doi: 10.1093/rfs/10.2.481 [16] Lando D (1998) On Cox Processes and Credit-risky Securities. Rev Deriv Res, 1998, 2:99-120. [17] Lando D (2000) Some elements of rating based credit risk modeling. Adv Fixed-Income Valuat Tools 193-215. [18] Leland H, Toft KB (1996) Optimal capital structure,endogenous bankruptcy,and the term strcuture of credit spreads. J Financ 3: 987-1019. [19] Longstaff F, Schwartz E (1995) A Simple Approach to Valuing Risky Fixed and Floating Rate Debt. J Financ 50: 789-819. doi: 10.1111/j.1540-6261.1995.tb04037.x [20] Ladyzenskaja OA, Solonnikov VA, Uralceva NN (1968) Linear and Quasilinear Equations of Parabolicn Type. AMS Transl Math Monogr 23. [21] Liang J, Wu Y, Hu B (2016) Asymptotic Traveling Wave Solution for a Credit Rating Migration Problem. J Differ Equ 261: 1017-1045. [22] Liang J, Zeng ZK (2015) Pricing on Corporate Bonds with Credit Rating Migration under Structure Framework, Appl Math A J Chin Univ. [23] Liang J, Zhao YJ (2014) Utility Indifference Valuation of Corporate Bond with Credit Rating Migration by Structure Approach, preprint. [24] Merton RC (1974) On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. J Financ 29: 449-470. [25] Thomas L, Allen D, Morkel-Kingsbury N (2002) A hidden Markov chain model for the term structure of bond credit risk spreads. Int Rev Financ Anal 11: 311-329. doi: 10.1016/S1057-5219(02)00078-9 [26] Tsiveriotis K, Fernandes C (1998) Valuing convertible bonds with credit risk. J Fixed Income 8: 95-102. doi: 10.3905/jfi.1998.408243
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

Article outline

Figures(1)

• On This Site