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What Should You Pay to Cap your ARM?—A Note on Capped Adjustable Rate Mortgages

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  • Maj-Britt Nordfang

    (Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark)

Abstract

In this paper, an Adjustable Rate Mortgage (ARM) and a Fixed Rate Mortgage (FRM) are formalized and studied in a simple continuous-time setting under the assumption of a simple one-factor Affine Term Structure (ATS). Through an application of existing results from ATS theory, it is shown that when the short rate reaches a certain pre-determined boundary, the constant payment stream on a new FRM equals the payments on an existing ARM. Hereby, this paper provides a theoretical build-in cap on the formalized ARM. The finite boundary for the short-rate suggests that certain caps on ARMs should (in theory) be offered free of charge.

Suggested Citation

  • Maj-Britt Nordfang, 2017. "What Should You Pay to Cap your ARM?—A Note on Capped Adjustable Rate Mortgages," IJFS, MDPI, vol. 5(1), pages 1-10, March.
    • Handle: RePEc:gam:jijfss:v:5:y:2017:i:1:p:10-:d:92294
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    References listed on IDEAS

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    4. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    5. Dahlquist, Magnus, 1996. "On alternative interest rate processes," Journal of Banking & Finance, Elsevier, vol. 20(6), pages 1093-1119, July.
    6. Martin Keller-Ressel & Thomas Steiner, 2008. "Yield curve shapes and the asymptotic short rate distribution in affine one-factor models," Finance and Stochastics, Springer, vol. 12(2), pages 149-172, April.
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