PREPAYMENT OPTION OF A PERPETUAL CORPORATE LOAN: THE IMPACT OF THE FUNDING COSTS

Timothee Papin and Gabriel Turinici ()
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Timothee Papin: BNP Paribas CIB Resource Portfolio Management and CEREMADE, Université Paris Dauphine, 75016 Paris, France
Gabriel Turinici: CEREMADE, Université Paris Dauphine, 75775 Paris, Cedex 16, France

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 04, 1-32

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 Cox–Ingersoll–Ross (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: 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; 91G20; 91G30; 91G40; 91G50; 91G60; 91G80; 93E20 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (5)

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DOI: 10.1142/S0219024914500289

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