Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Chernogorova, T., Koleva, M., Valkov, R.: A two-grid penalty method for American options. Comp. Appl. Math. (2018). https://doi.org/10.1007/s40314-017-0457-6
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 146745
Gyulov, T., Valkov, R.: American option pricing problem transformed on finite interval. Intern. J. of Comp. Math. 93, 821–836 (2016)
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)
Jiang, L.: Modeling and Methods for Option Pricing. World Scientific, Singapore (2005)
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). https://doi.org/10.1007/978-3-642-18466-6_54
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). https://doi.org/10.1007/978-3-642-29843-1_63
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). https://doi.org/10.1007/978-3-319-61282-9_11
Kwok, J.: Mathematical Models of Financial Derivatives. Springer, Heidelberg (1998). https://doi.org/10.1007/978-3-540-68688-0
Leland, H.: Corporate debt value, bond covenants, and optimal capital structure. J. Finance 49(4), 1213–1252 (1994)
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)
Liang, J., Zhao, Y.J.: Utility indifference valuation of corporate bond with credit rating migration by structure approach. Econ. Model. 54, 339–346 (2016)
Zhu, S.-P., Zang, J.: A new predictor-corrector scheme for valuing American puts. Appl. Math. Comput. 2017, 4439–4452 (2011)
Acknowledgements
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Kandilarov, J., Vulkov, L. (2019). Front Fixing Finite Difference Method for Pricing a Corporate Bond with Credit Rating Migration. In: Nikolov, G., Kolkovska, N., Georgiev, K. (eds) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science(), vol 11189. Springer, Cham. https://doi.org/10.1007/978-3-030-10692-8_47
Download citation
DOI: https://doi.org/10.1007/978-3-030-10692-8_47
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-10691-1
Online ISBN: 978-3-030-10692-8
eBook Packages: Computer ScienceComputer Science (R0)