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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Timothée Papin & Gabriel Turinici, 2014. "Prepayment option of a perpetual corporate loan: the impact of the funding costs," Post-Print hal-00768571, HAL.
    • Handle: RePEc:hal:journl:hal-00768571
    DOI: 10.1142/S0219024914500289
    Note: View the original document on HAL open archive server: https://hal.science/hal-00768571v3
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    References listed on IDEAS

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    10. repec:dau:papers:123456789/7818 is not listed on IDEAS
    11. Timothee Papin & Gabriel Turinici, 2013. "Valuation of the Prepayment Option of a Perpetual Corporate Loan," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, March.
    12. Yong Chen & Michael Connolly & Wenjin Tang & Tie Su, 2009. "The value of mortgage prepayment and default options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(9), pages 840-861, September.
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    14. Timothée Papin & Gabriel Turinici, 2013. "Valuation of the Prepayment Option of a Perpetual Corporate Loan," Post-Print hal-00653041, HAL.
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    Cited by:

    1. Milan Kumar Das & Anindya Goswami, 2019. "Testing of binary regime switching models using squeeze duration analysis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-20, March.
    2. Milan Kumar Das & Anindya Goswami & Sharan Rajani, 2019. "Inference of Binary Regime Models with Jump Discontinuities," Papers 1910.10606, arXiv.org, revised Mar 2022.
    3. Milan Kumar Das & Anindya Goswami, 2018. "Testing of Binary Regime Switching Models using Squeeze Duration Analysis," Papers 1807.04393, arXiv.org, revised Aug 2018.
    4. Biswas, Arunangshu & Goswami, Anindya & Overbeck, Ludger, 2018. "Option pricing in a regime switching stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 116-126.
    5. Arunangshu Biswas & Anindya Goswami & Ludger Overbeck, 2017. "Option Pricing in a Regime Switching Stochastic Volatility Model," Papers 1707.01237, arXiv.org, revised Jan 2018.

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