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

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Author Info

  • Timothée Papin

    ()
    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine)

  • Gabriel Turinici

    ()
    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine)

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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.

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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00768571.

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    Date of creation: 21 Dec 2012
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    Handle: RePEc:hal:wpaper:hal-00768571

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00768571
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    Web page: http://hal.archives-ouvertes.fr/

    Related research

    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.;

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    1. Robert Elliott & Tak Kuen Siu, 2009. "On Markov-modulated Exponential-affine Bond Price Formulae," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 1-15.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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