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

Posted: 12 Nov 2008 Last revised: 16 Mar 2010

See all articles by Takaaki Ozeki

Takaaki Ozeki

Mizuho-DL Financial Technology Co., Ltd.

Yuji Umezawa

Mizuho-DL Financial Technology Co., Ltd.

Akira Yamazaki

Hosei University - Graduate School of Business Administration

Daisuke Yoshikawa

Hokkai-Gakuen University

Date Written: August 28, 2008

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 formulas very accurate and useful in practice.

Keywords: Residential Mortgage-Backed Security, Prepayment Risk, Proportional Hazard Model, Cumulant Expansion

JEL Classification: G12,G13

Suggested Citation

Ozeki, Takaaki and Umezawa, Yuji and Yamazaki, Akira and Yoshikawa, Daisuke, Valuation of Residential Mortgage-Backed Securities with Proportional Hazard Model: Cumulant Expansion Approach to Pricing RMBS (August 28, 2008). Journal of Fixed Income, Vol. 18, No. 4, 2009. Available at SSRN: https://ssrn.com/abstract=1299346

Takaaki Ozeki

Mizuho-DL Financial Technology Co., Ltd. ( email )

Japan

Yuji Umezawa

Mizuho-DL Financial Technology Co., Ltd. ( email )

Japan

Akira Yamazaki (Contact Author)

Hosei University - Graduate School of Business Administration ( email )

Japan

Daisuke Yoshikawa

Hokkai-Gakuen University ( email )

4-1-40, Asahi-machi, Toyohira-ku
Sapporo-shi
Hokkai-do, 062-8605
Japan

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