Front Fixing Finite Difference Method for Pricing a Corporate Bond with Credit Rating Migration

  • Juri KandilarovEmail author
  • Lubin Vulkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11189)


A front fixing finite difference method for pricing a corporate bond with credit rating migration is developed. Two algorithms are proposed: the first one is of a predictor-corrector type while the second one is a Newton-like method. Comparison numerical experiments show the efficiency and effectiveness of the numerical algorithms.


Corporate bond-pricing model Credit-rating migration Free boundary problem Finite difference scheme Predictor-corrector method Newton method 



This work was partially supported by the Project 2018-FNSE-03 of the University of Ruse and by the Bulgarian National Fund of Science under the Project DN 12/4-2017.


  1. 1.
    Chernogorova, T., Koleva, M., Valkov, R.: A two-grid penalty method for American options. Comp. Appl. Math. (2018). Scholar
  2. 2.
    Company, R., Egorova, V.N., Jodar, L.: Solving American option pricing models by the front fixing method: numerical analysis and computing. Abstr. Appl. Anal. 2014 (2014). Article ID 146745MathSciNetCrossRefGoogle Scholar
  3. 3.
    Gyulov, T., Valkov, R.: American option pricing problem transformed on finite interval. Intern. J. of Comp. Math. 93, 821–836 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Hu, B., Liang, J., Wu, Y.: A free boundary problem for corporate bond with credit rating migration. J. Math. Anal. Appl. 428(2), 896–909 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Jiang, L.: Modeling and Methods for Option Pricing. World Scientific, Singapore (2005)CrossRefGoogle Scholar
  6. 6.
    Kandilarov, J.D., Valkov, R.L.: A numerical approach for the American call option pricing model. In: Dimov, I., Dimova, S., Kolkovska, N. (eds.) NMA 2010. LNCS, vol. 6046, pp. 453–460. Springer, Heidelberg (2011). Scholar
  7. 7.
    Kandilarov, J.D., Ševčovič, D.: Comparison of two numerical methods for computation of American type of the floating strike Asian option. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2011. LNCS, vol. 7116, pp. 558–565. Springer, Heidelberg (2012). Scholar
  8. 8.
    Koleva, M.N., Valkov, R.L.: Modified barrier penalization method for pricing American options. In: Ehrhardt, M., Günther, M., ter Maten, E.J.W. (eds.) Novel Methods in Computational Finance. MI, vol. 25, pp. 215–226. Springer, Cham (2017). Scholar
  9. 9.
    Kwok, J.: Mathematical Models of Financial Derivatives. Springer, Heidelberg (1998). Scholar
  10. 10.
    Leland, H.: Corporate debt value, bond covenants, and optimal capital structure. J. Finance 49(4), 1213–1252 (1994)CrossRefGoogle Scholar
  11. 11.
    Liang, J., Chen, X., Wu, Y., Yin, H.-M.: On a corporate bond pricing model with credit rating migration risks and stochastic interest rate. Quant. Financ. Econ. 1(3), 300–319 (2017)CrossRefGoogle Scholar
  12. 12.
    Liang, J., Zhao, Y.J.: Utility indifference valuation of corporate bond with credit rating migration by structure approach. Econ. Model. 54, 339–346 (2016)CrossRefGoogle Scholar
  13. 13.
    Zhu, S.-P., Zang, J.: A new predictor-corrector scheme for valuing American puts. Appl. Math. Comput. 2017, 4439–4452 (2011)MathSciNetzbMATHGoogle Scholar

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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of RuseRuseBulgaria

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