IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2410.21110.html
   My bibliography  Save this paper

Modeling and Replication of the Prepayment Option of Mortgages including Behavioral Uncertainty

Author

Listed:
  • Leonardo Perotti
  • Lech A. Grzelak
  • Cornelis W. Oosterlee

Abstract

Prepayment risk embedded in fixed-rate mortgages forms a significant fraction of a financial institution's exposure, and it receives particular attention because of the magnitude of the underlying market. The embedded prepayment option (EPO) bears the same interest rate risk as an exotic interest rate swap (IRS) with a suitable stochastic notional. We investigate the effect of relaxing the assumption of a deterministic relationship between the market interest rate incentive and the prepayment rate. A non-hedgeable risk factor is modeled to capture the uncertainty in mortgage owners' behavior, leading to an incomplete market. We prove under natural assumptions that including behavioral uncertainty reduces the exposure's value. We statically replicate the exposure resulting from the EPO with IRSs and swaptions, and we show that a replication based on swaps solely cannot easily control the right tail of the exposure distribution, while including swaptions enables that. The replication framework is flexible and focuses on different regions in the exposure distribution. Since a non-hedgeable risk factor entails the existence of multiple equivalent martingale measures, pricing and optimal replication are not unique. We investigate the effect of a market price of risk misspecification and we provide a methodology to generate robust hedging strategies. Such strategies, obtained as solutions to a saddle-point problem, allow us to bound the exposure against a misspecification of the pricing measure.

Suggested Citation

  • Leonardo Perotti & Lech A. Grzelak & Cornelis W. Oosterlee, 2024. "Modeling and Replication of the Prepayment Option of Mortgages including Behavioral Uncertainty," Papers 2410.21110, arXiv.org.
    • Handle: RePEc:arx:papers:2410.21110
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2410.21110
    File Function: Latest version
    Download Restriction: no
    ---><---

    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. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    4. Balter, Anne G. & Pelsser, Antoon, 2020. "Pricing and hedging in incomplete markets with model uncertainty," European Journal of Operational Research, Elsevier, vol. 282(3), pages 911-925.
    5. René Aïd & Luciano Campi & Adrien Nguyen Huu & Nizar Touzi, 2009. "A Structural Risk-Neutral Model Of Electricity Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 925-947.
    6. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    7. Emanuele Casamassima & Lech A. Grzelak & Frank A. Mulder & Cornelis W. Oosterlee, 2022. "Pricing And Hedging Prepayment Risk In A Mortgage Portfolio," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 25(04n05), pages 1-37, June.
    8. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    9. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    2. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    3. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.
    4. Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.
    5. Dariusz Gatarek & Juliusz Jabłecki, 2021. "Between Scylla and Charybdis: The Bermudan Swaptions Pricing Odyssey," Mathematics, MDPI, vol. 9(2), pages 1-32, January.
    6. Marat Kramin & Timur Kramin & Stephen Young & Venkat Dharan, 2005. "A Simple Induction Approach and an Efficient Trinomial Lattice for Multi-State Variable Interest Rate Derivatives Models," Review of Quantitative Finance and Accounting, Springer, vol. 24(2), pages 199-226, January.
    7. Eickholt, Mathias & Entrop, Oliver & Wilkens, Marco, 2014. "Individual investors and suboptimal early exercises in the fixed-income market," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe 14, University of Passau, Faculty of Business and Economics.
    8. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2015. "Stochastic string models with continuous semimartingales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 229-246.
    9. Ravi Kashyap, 2022. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Annals of Operations Research, Springer, vol. 315(2), pages 1175-1215, August.
    10. Ronald Hochreiter & Georg Pflug, 2006. "Polynomial Algorithms for Pricing Path-Dependent Interest Rate Instruments," Computational Economics, Springer;Society for Computational Economics, vol. 28(3), pages 291-309, October.
    11. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    12. Lin, Bing-Huei, 1999. "Fitting the term structure of interest rates for Taiwanese government bonds," Journal of Multinational Financial Management, Elsevier, vol. 9(3-4), pages 331-352, November.
    13. Matteo Bissiri & Riccardo Cogo, 2017. "Behavioral Value Adjustments," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-37, December.
    14. Robert R. Bliss & Ehud I. Ronn, 1997. "Callable U.S. Treasury bonds: optimal calls, anomalies, and implied volatilities," FRB Atlanta Working Paper 97-1, Federal Reserve Bank of Atlanta.
    15. Tucker, A. L. & Wei, J. Z., 1998. "Valuation of LIBOR-Contingent FX options," Journal of International Money and Finance, Elsevier, vol. 17(2), pages 249-277, April.
    16. Kimmel, Robert L., 2004. "Modeling the term structure of interest rates: A new approach," Journal of Financial Economics, Elsevier, vol. 72(1), pages 143-183, April.
    17. Roberto Baviera, 2017. "Back-of-the-envelope swaptions in a very parsimonious multicurve interest rate model," Papers 1712.06466, arXiv.org.
    18. Issler, João Victor, 1995. "Estimating the term structure of volatility and fixed income derivative pricing," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 272, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    19. Chen An & Mahayni Antje B., 2008. "Endowment Assurance Products: Effectiveness of Risk-Minimizing Strategies under Model Risk," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 2(2), pages 1-29, March.
    20. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2410.21110. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.