Behaviour of bond’s embedded option with regard to credit rating

    Bohumil Stádník Affiliation


In this financial engineering research, we study the behaviour of an option premium of a call/put option which is embedded in a typical fixed coupon bond with finite maturity. The contribution of the research is the conclusion about the dynamics of premium changes; represented by direction and sensitivity; with respect to the changes in credit rating and also risk-free interest rate development. The aim of the research is also to clearly demonstrate this theoretically complicated topic to the financial practitioners using a practical example. We are about to consider a 3-dimensional process where the dimensions are: time, rating development process and risk-free interest rate development. We use Standard & Poor’s rating transition matrix to create rating tree and Hull-White model for modelling of risk-free interest rate development. We add embedded call/put option to the bond structure and assume the call/put option to be exercised in case of interest rates decline/rise or rating worsening/improvement. For valuation, we use the risk-neutral concept. Using a numerical solution on the 3-dimensional tree (implemented in MATLAB), we avoid problems that appear while analytical solving of partial differential equations.

Keyword : embedded call/put option, credit rating transition, more dimensional tree, Standard & Poor’s rating, bedded option premium, rating development process

How to Cite
Stádník, B. (2018). Behaviour of bond’s embedded option with regard to credit rating. Business: Theory and Practice, 19, 261-270.
Published in Issue
Nov 16, 2018
Abstract Views
PDF Downloads
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.


Acerbi C, Tasche D (2002) On the coherence of expected shortfall. Journal of Banking and Finance 26: 1487-1503.

Aguais SD, Forest LR (2000) The future of risk-adjusted credit pricing in financial institutions. RMA Journal, 26-31.

Aguais SD, Forest LR, Rosen D (2000) Building a credit risk valuation framework for loan instruments. Algo Research Quarterly 3: 21-46.

Aguais SD, Santomero AM (1998) Incorporating new fixed in- come approaches into commerical loan valuation. Journal of Lending & Credit Risk Management, 58-65.

Artzner PF, Dalbaen J, Eber M, Heath B (1999) Coherent mea- sures of risk. Mathematical Finance 9: 203-228. https://doi. org/10.1111/1467-9965.00068

Brigo D, Mercurio F (2006) Interest rate models – theory and practice (2nd ed). New York: Springer Berlin Heidelberg.

Castagna A, Mercurio F, Mosconi P (2009) Analytical credit VaR with stochastic probabilities of default and recoveries. Working paper.

Choro’s-Tomczyk B, Härdle WK, Okhrin O (2016) A semipara- metric factor model for cdo surfaces dynamics. Journal of Multivariate Analysis 146: 151-163.

Ciochetti B, Deng Y, Gao B, Yao R (2002) The termination of mortgage contracts through prepayment and default in the commercial mortgage markets a proportional hazard appro- ach with competing risks. Real Estate Economics 30: 595-633.

Cont R, Minca A (2013) Recovering portfolio default intensities implied by cdo quotes. Mathematical Finance 23 (1): 94-121.

Dozsa M, Janda K (2017) Corporate asset pricing models and debt contracts. In: Pinto A, Zilberman D (Eds) Modeling, dynamics, optimization and bioeconomics II. Springer Pro- ceedings in Mathematics and Statistics, 183-222. https://doi. org/10.1007/978-3-319-55236-1_11

Engelmann B, Rauhmeier R (2006) The Basel II risk parameters: estimation, validation, and stress testing. Springer Berlin Heidelberg New York.

Gupton GM, Finger CC, Bhatia M (1997) CreditMetrics – Tech- nical Document, Working paper, Morgan Guaranty Trust Co.

Hirsa A (2016) Computational methods in finance. Chapman and Hall/CRC Financial Mathematics Series. CRC Press.

Horváth R, Teplý P (2013) Risk management of building socie- ties in the Czech Republic. Ekonomický časopis/Journal of Economics 61 (1): 24-46.

Janda K, Michalikova E, Skuhrovec J (2013) Credit support for export: robust evidence from the Czech Republic. The World Economy 36 (12): 1588-1610. twec.12061

Janda K, Rojcek J (2014) Bankruptcy triggering asset value continuous time finance approach. In: Pinto A, Zilberman D (Eds) Modeling, dynamics, optimization and bioeconomics I. Springer Proceedings in Mathematics and Statistics 73: 357- 382.

Jarrow RA, Lando D, Turnbull S (1997) A Markov model for the term structure of credit spreads. Review of Financial Studies 10: 481-523.

Kalkbrener M (2005) An axiomatic approach to capital allocation. Mathematical Finance 15: 425-437.

Kalkbrener M, Lotter H, Overbeck L (2004) Sensible and efficient capital allocation for credit portfolios, risk 17: 19-24.