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A prepayment model of mortgage-backed securities based on unobservable prepayment cost processes

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Advances in Mathematical Economics

Part of the book series: Advances in Mathematical Economics ((MATHECON,volume 8))

Abstract

We propose a prepayment model of mortgage based on a structural approach in order to analyze prepayment risk of mortgage-backed securities (MBS). We introduce a continuous process named prepayment cost process. Specifically, each mortgager’s prepayment time is defined by the first time when her or his prepayment cost process falls below zero, but prepayment cost processes are supposed to be unobservable in the market. We also introduce a risk unique to each loan pool of mortgages, called a loan pool risk (LPR), and we regard LPR as a systematic risk other than interest rate. Using the model, we discuss the conditional distribution of prepayment times and a risk-neutral valuation of pass-through MBS. It is shown that each mortgager’s conditional non-prepayment probability and the posterior distribution of LPR play quite important roles in our study.

This is a summary version of the original paper [24]

This research is partially supported by Grant-in-Aid for Young Scientists (B) No. 16710108 from the Ministry of Education, Culture, Sports, Science and Technology.

Please refer to the original paper [24] for detailed discussion as well as some illustrations of numerical experiment on simulation.

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Author information

Authors and Affiliations

  1. Graduate School of Innovation Management, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8552, Japan

    Hidetoshi Nakagawa

  2. Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd., 2-5-6 Shiba, Minato-ku, Tokyo, 105-0014, Japan

    Tomoaki Shouda

  3. Graduate School of International Corporate Strategy, Hitotsubashi University, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8439, Japan

    Tomoaki Shouda

Authors
  1. Hidetoshi Nakagawa
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  2. Tomoaki Shouda
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Editors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-0041, Japan

    Shigeo Kusuoka (Professor) (Professor)

  2. Graduate Faculty of Economics, Hitotsubashi University, Kunitachi, Tokyo, 186-8601, Japan

    Akira Yamazaki (Professor) (Professor)

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© 2006 Springer-Verlag

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Nakagawa, H., Shouda, T. (2006). A prepayment model of mortgage-backed securities based on unobservable prepayment cost processes. In: Kusuoka, S., Yamazaki, A. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 8. Springer, Tokyo. https://doi.org/10.1007/4-431-30899-7_15

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