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Journal of Information Science and Engineering, Vol. 31 No. 3, pp. 925-942 (May 2015)


Outstanding Principal as Prepayment Value: A Closed-Form Formula for Mortgage Pricing*


YI-CHENG TSAI1,2, CHIN-LAUNG LEI1, JAN-MING HO2, MING-YANG KAO3 AND SZU-LANG LIAO4
1Electrical Engineering and Computer Science
National Taiwan University
Taipei, 116 Taiwan
2Institute of Information Science
Academia Sinica
Taipei, 115 Taiwan
3Electrical Engineering and Computer Science
Northwestern University
Evanston, IL 60201, USA
4Department of Money and Banking
National Chung-Cheng University
Taipei, 621 Taiwan
E-mail: yicheng@iis.sinica.edu.tw; lei@cc.ee.ntu.edu.tw;
hoho@iis.sinica.edu.tw; kao@northwestern.edu; liaosl@nccu.edu.tw

Mortgage is one of the most popular instruments in the financial markets. In this study, we consider three actions, i.e., to default, to prepay, and to maintain the mortgage, that a borrower may have in mortgage horizon. We provide an effective pricing formula, which not only considers the effect that default might affect the mortgage value, but also accurately computes the impact due to prepayment risk. Our model defines the prepayment value of the mortgage as the amount of outstanding principal, in contrast to defining prepayment value as a constant proportion of maintaining value of the mortgage. We present a new closed-form pricing formula of risky mortgage and also derive its yield to maturity, duration and convexity to provide a framework for risk management.

Keywords: mortgage, prepayment, default, yield to maturity, duration, convexity, risk management

Full Text () Retrieve PDF document (201505_09.pdf)

Received November 29, 2013; reviesed March 15, 2014; accepted April 22, 2014.
Communicated by Meng-Chan Chen.
* Partial results of this paper was presented at the Computational Intelligence for Financial Engineering and Economics (CIFEr), 2012 IEEE Conference, New York, 29-30 March 2012.