A Semi Discrete Model for Mortgage Valuation and Its Computation by an Adaptive Finite Element Method
Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 6 : pp. 831–851
Abstract
In traditional models for valuation of mortgages with a stochastic interest rate, one parabolic equation starting from the maturity is assumed to govern the whole life of a mortgage. Following the valuation of zero-coupon bond, a new model is proposed, where an initial value problem is restarted after a mortgage payment each month. In addition, the low and high limits on the interest rate are incorporated into the initial-boundary value problems, so that the partial differential equation remains regular and the solution better approximates the real value. We show the existence and uniqueness of the solution and the free boundary (which determines early prepayment). A finite element method is introduced with a convergence analysis. Numerical tests are presented and the results are interpreted for guiding mortgage practice.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-468
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 6 : pp. 831–851
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Finite element method parabolic equation free boundary problem mortgage valuation.