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

Timothée Papin () and Gabriel Turinici ()
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Timothée Papin: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Gabriel Turinici: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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Abstract: 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.

Keywords: Markov modulated dynamics; 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. (search for similar items in EconPapers)
Date: 2014-06-13
New Economics Papers: this item is included in nep-ban
Note: View the original document on HAL open archive server: https://hal.science/hal-00768571v3
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Citations: View citations in EconPapers (5)

Published in International Journal of Theoretical and Applied Finance, 2014, 17 (04), pp.1450028. ⟨10.1142/S0219024914500289⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00768571

DOI: 10.1142/S0219024914500289

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