Xie, Dejun
(2007)
Optimal Strategy for Prepayment of Mortgages.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
We study a borrower's optimal strategies to terminate a mortgage with a fixed interest rate by paying the outstanding balance all at once. The problem is modelled as a free boundary problem for a Black-Scholes type pricing equation under the assumption of the Vasicek model for the short rate of investment. Here the free boundary provides the optimal time at which the mortgage contract is to be terminated. A number of integral identities are derived and then used to design efficient numerical codes for computing thefree boundary. Fornumerical simulation, parameters for the Vasicek model areestimated via the method of maximum likelihood estimate using 40 years of datafrom US government bonds. The asymptotic behavior of the freeboundary for the infinite horizon is fully analyzed. Interpolatingthis infinite horizon behavior and a known near expiry behavior, two simple analytical approximation formulas for the optimalexercise boundary are proposed. Numerical evidence shows that theenhanced version of the approximation formula is amazinglyaccurate; in general, its relative error is less than $1\%$, forall time before expiry.
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| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
27 September 2007 |
| Date Type: |
Completion |
| Defense Date: |
6 April 2007 |
| Approval Date: |
27 September 2007 |
| Submission Date: |
3 July 2007 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| 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: |
approximation formula; asymptotic behavior; free boundary problem; interest rate; optimal strategy; mortgage; prepayment |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-07032007-152940/, etd-07032007-152940 |
| Date Deposited: |
10 Nov 2011 19:49 |
| Last Modified: |
15 Nov 2016 13:45 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/8256 |
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