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Valuation of Residential Mortgage-Backed Securities with Proportional Hazard Model: Cumulant Expansion Approach to Pricing RMBS

Takaaki Ozeki, Yuji Umezawa, Akira Yamazaki and Daisuke Yoshikawa
The Journal of Fixed Income Spring 2009, 18 (4) 62-77; DOI: https://doi.org/10.3905/JFI.2009.18.4.062
Takaaki Ozeki
is a senior financial engineer at Mizuho-DL Financial Technology Co., Ltd., in Tokyo, Japan.
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  • For correspondence: takaaki-ozeki@fintec.co.jp
Yuji Umezawa
is a financial engineer at Mizuho-DL Financial Technology Co., Ltd., in Tokyo, Japan.
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  • For correspondence: yuji-umezawa@fintec.co.jp
Akira Yamazaki
is a senior financial engineer at Mizuho-DL Financial Technology Co., Ltd., in Tokyo, Japan.
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  • For correspondence: akira-yamazaki@fintec.co.jp
Daisuke Yoshikawa
is a senior financial engineer at Mizuho-DL Financial Technology Co., Ltd., in Tokyo, Japan.
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  • For correspondence: daisuke-yoshikawa@fintec.co.jp
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Abstract

This paper proposes a pricing formula for residential mortgage-backed securities (RMBS) with the proportional hazard model. First, we develop basic models of mortgage contracts with prepayment risk in the intensity-based framework. Next, assuming the proportional hazard model to describe prepayment risk, which is used as a typical prepayment model both academically and in practice; a general pricing formula for not only RMBS, but also IO and PO is derived by using the cumulant expansion method. Furthermore, it is also shown that the formula is applicable to various types of the proportional hazard models. Finally, numerical examples based on Japanese RMBS market data demonstrate that the formula is very accurate and useful in practice.

TOPICS: MBS and residential mortgage loans, credit risk management, big data/machine learning, developed markets [Japan]

  • © 2009 Pageant Media Ltd
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The Journal of Fixed Income
Vol. 18, Issue 4
Spring 2009
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Valuation of Residential Mortgage-Backed Securities with Proportional Hazard Model: Cumulant Expansion Approach to Pricing RMBS
Takaaki Ozeki, Yuji Umezawa, Akira Yamazaki, Daisuke Yoshikawa
The Journal of Fixed Income Mar 2009, 18 (4) 62-77; DOI: 10.3905/JFI.2009.18.4.062

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Valuation of Residential Mortgage-Backed Securities with Proportional Hazard Model: Cumulant Expansion Approach to Pricing RMBS
Takaaki Ozeki, Yuji Umezawa, Akira Yamazaki, Daisuke Yoshikawa
The Journal of Fixed Income Mar 2009, 18 (4) 62-77; DOI: 10.3905/JFI.2009.18.4.062
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  • Article
    • Abstract
    • MODELS
    • MORTGAGE CONTRACTS WITH PREPAYMENT IN THE INTENSITY-BASED FRAMEWORK
    • PRICING FORMULA
    • STOCHASTIC PROPORTIONAL HAZARD MODELS
    • NUMERICAL EXAMPLES
    • CONCLUDING REMARKS
    • ENDNOTES
    • REFERENCES
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