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Pricing and Hedging Prepayment Risk in a Mortgage Portfolio

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Listed:
  • Emanuele Casamassima
  • Lech A. Grzelak
  • Frank A. Mulder
  • Cornelis W. Oosterlee

Abstract

Understanding mortgage prepayment is crucial for any financial institution providing mortgages, and it is important for hedging the risk resulting from such unexpected cash flows. Here, in the setting of a Dutch mortgage provider, we propose to include non-linear financial instruments in the hedge portfolio when dealing with mortgages with the option to prepay part of the notional early. Based on the assumption that there is a correlation between prepayment and the interest rates in the market, a model is proposed which is based on a specific refinancing incentive. The linear and non-linear risks are addressed by a set of tradeable instruments in a static hedge strategy. We will show that a stochastic model for the notional of a mortgage unveils non-linear risk embedded in a prepayment option. Based on a calibration of the refinancing incentive on a data set of more than thirty million observations, a functional form of the prepayments is defined, which accurately reflects the borrowers' behaviour. We compare this functional form with a fully rational model, where the option to prepay is assumed to be exercised rationally.

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  • Emanuele Casamassima & Lech A. Grzelak & Frank A. Mulder & Cornelis W. Oosterlee, 2021. "Pricing and Hedging Prepayment Risk in a Mortgage Portfolio," Papers 2109.14977, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2109.14977
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    References listed on IDEAS

    as
    1. Erwin Charlier & Arjan Van Bussel, 2003. "Prepayment Behavior of Dutch Mortgagors: An Empirical Analysis," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 31(2), pages 165-204, June.
    2. Andrew Kalotay & Deane Yang & Frank J. Fabozzi, 2004. "An Option-Theoretic Prepayment Model For Mortgages And Mortgage-Backed Securities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(08), pages 949-978.
    3. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, June.
    4. Sumit Agarwal & John C. Driscoll & David I. Laibson, 2013. "Optimal Mortgage Refinancing: A Closed‐Form Solution," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(4), pages 591-622, June.
    5. Cornelis W Oosterlee & Lech A Grzelak, 2019. "Mathematical Modeling and Computation in Finance:With Exercises and Python and MATLAB Computer Codes," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number q0236, February.
    6. Dunn, Kenneth B & McConnell, John J, 1981. "A Comparison of Alternative Models for Pricing GNMA Mortgage-Backed Securities," Journal of Finance, American Finance Association, vol. 36(2), pages 471-484, May.
    7. repec:mcb:jmoncb:v:45:y:2013:i::p:591-622 is not listed on IDEAS
    8. Bart H. M. Kuijpers & Peter C. Schotman, 2007. "Optimal prepayment of Dutch mortgages," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(1), pages 137-155, February.
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