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Optimal Mortgage Prepayment Under the Cox-Ingersoll-Ross Model

Jones, Christopher (2013) Optimal Mortgage Prepayment Under the Cox-Ingersoll-Ross Model. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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We study a parabolic variational inequality and associated free boundary problem (FBP) with financial applications. We consider a mortgage contract having the early termination option via prepayment under the Cox-Ingersoll-Ross (CIR) model for the short rate. The problem is of significant interest from both mathematical and economic points of view. The main difficulty is that the Black-Scholes-type partial differential equation (PDE) associated with the problem is not uniformly parabolic and therefore standard approaches have to be modified to treat the degeneracy of the PDE.

Our main results are the existence and uniqueness of a solution to the variational inequality and the associated FBP; the free boundary represents optimal prepayment rate for the mortgage contract at each time prior to expiry. We establish regularity of the free boundary; several other properties of the free boundary are studied as well as the infinite horizon problem.

From the financial point of view, the infinite horizon problem is interpreted as the mortgage prepayment problem when there is a long time to expiration. In solving the infinite horizon problem we obtain a critical rate, such that for mortgage rates below this critical rate, prepayment is never an optimal decision for a long times to expiration.

With the existence of a unique solution to the FBP established, we conclude by performing a calibration of the CIR model to constant maturity Treasury yields and investigate numerical aspects of the variational inequality.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Jones, Christophercsj3@pitt.eduCSJ3
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairChen, Xinfuxinfu@pitt.eduXINFU
Committee MemberChadam, Johnchadam@pitt.eduCHADAM
Committee MemberJiang, Huiqianghqjiang@pitt.eduHQJIANG
Committee MemberRichard, Jean-Francoisfantin@pitt.eduFANTIN
Date: 29 January 2013
Date Type: Publication
Defense Date: 24 August 2012
Approval Date: 29 January 2013
Submission Date: 5 December 2012
Access Restriction: 5 year -- Restrict access to University of Pittsburgh for a period of 5 years.
Number of Pages: 88
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Mathematical Finance
Date Deposited: 29 Jan 2013 19:28
Last Modified: 29 Jan 2018 06:15


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