Communications in Mathematical Sciences

Volume 9 (2011)

Number 4

On the strong solution of a class of partial differential equations that arise in the pricing of mortgage backed securities

Pages: 1033 – 1050

DOI: http://dx.doi.org/10.4310/CMS.2011.v9.n4.a5

Authors

Nathaniel S. Barlow (Center for Computational Research, State Universty of New York at Buffalo)

Dervis Bayazit (Federal Home Loan Bank of Atlanta, Atlanta, Georgia, U.S.A.)

Rana D. Parshad (Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia)

Ramchandra Prasad V. (Department of Mathematics, Madanapalle Institute of Technology and Science, Andhra Pradesh, India)

Abstract

We consider a reduced form pricing model for mortgage backed securities, formulated as a non-linear partial differential equation. We prove that the model possesses a weak solution. We then show that under additional regularity assumptions on the initial data, we also have a mild solution. This mild solution is shown to be a strong solution via further regularity arguments. We also numerically solve the reduced model via a Fourier spectral method. Lastly, we compare our numerical solution to real market data. We observe interestingly that the reduced model captures a number of recent market trends in this data, that have escaped previous models.

Keywords

mortgage backed security, reduced modeling, mild solution, strong solution, Fourier spectral method

2010 Mathematics Subject Classification

35A01, 35D35, 76M22, 91G20, 91G80

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