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Prepayment option of a perpetual corporate loan: the impact of the funding costs

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Date
2014
Dewey
Economie financière
Sujet
loan prepayment; American option; prepayment option; funding costs; mortgage option; perpetual option; variational inequality; option pricing; CIR process; switching regimes; liquidity regime; Markov modulated dynamics
JEL code
G12
Journal issue
International Journal of Theoretical and Applied Finance
Volume
17
Number
4
Publication date
2014
Publisher
World Scientific
DOI
http://dx.doi.org/10.1142/S0219024914500289
URI
https://basepub.dauphine.fr/handle/123456789/13377
Collections
  • CEREMADE : Publications
Metadata
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Author
Papin, Timothée
Turinici, Gabriel
Type
Article accepté pour publication ou publié
Abstract (EN)
We 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.

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