Prepayment option of a perpetual corporate loan: the impact of the funding costs
AbstractWe investigate in this paper a perpetual prepayment option related to a corporate loan. The short interest rate and default intensity of the firm are supposed to follow CIR processes. A liquidity term that represents the funding costs of the bank is introduced and modeled as a continuous time discrete state Markov chain. The prepayment option needs specific attention as the payoff itself is a derivative product and thus an implicit function of the parameters of the problem and of the dynamics. We prove verification results that allows to certify the geometry of the exercise region and compute the price of the option. We show moreover that the price is the solution of a constrained minimization problem and propose a numerical algorithm building on this result. The algorithm is implemented in a two-dimensional code and several examples are considered. It is found that the impact of the prepayment option on the loan value is not to be neglected and should be used to assess the risks related to client prepayment. Moreover the Markov chain liquidity model is seen to describe more accurately clients' prepayment behavior than a model with constant liquidity.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by HAL in its series Working Papers with number hal-00768571.
Date of creation: 21 Dec 2012
Date of revision:
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00768571
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
funding costs; liquidity regime; loan prepayment; mortgage option; American option; perpetual option; option pricing; variational inequality; prepayment option; CIR process; switching regimes; Markov modulated dynamics.;
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Eduardo S. Schwartz & Walter N. Torous, 1993. "Mortgage Prepayment and Default Decisions: A Poisson Regression Approach," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 21(4), pages 431-449.
- Georges Dionne & Geneviève Gauthier & Khemais Hammami & Mathieu Maurice & Jean-Guy Simonato, 2010.
"A Reduced Form Model of Default Spreads with Markov-Switching Macroeconomic Factors,"
Cahiers de recherche
- Dionne, Georges & Gauthier, Geneviève & Hammami, Khemais & Maurice, Mathieu & Simonato, Jean-Guy, 2011. "A reduced form model of default spreads with Markov-switching macroeconomic factors," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1984-2000, August.
- Georges Dionne & Geneviève Gauthier & Khemais Hammami & Mathieu Maurice & Jean-Guy Simonato, 2007. "A Reduced Form Model of Default Spreads with Markov Switching Macroeconomic Factors," Cahiers de recherche 0741, CIRPEE.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
- Robert Elliott & Tak Kuen Siu, 2009. "On Markov-modulated Exponential-affine Bond Price Formulae," Applied Mathematical Finance, Taylor and Francis Journals, vol. 16(1), pages 1-15.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).
If references are entirely missing, you can add them using this form.