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

Handle URI:
http://hdl.handle.net/10754/561659
Title:
On the strong solution of a class of partial differential equations that arise in the pricing of mortgage backed securities
Authors:
Parshad, Rana ( 0000-0001-7443-8927 ) ; Bayazit, Derviş; Barlow, Nathaniel S.; Prasad, V. Ramchandra
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.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
International Press of Boston
Journal:
Communications in Mathematical Sciences
Issue Date:
2011
DOI:
10.4310/cms.2011.v9.n4.a5
Type:
Article
ISSN:
15396746
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorParshad, Ranaen
dc.contributor.authorBayazit, Dervişen
dc.contributor.authorBarlow, Nathaniel S.en
dc.contributor.authorPrasad, V. Ramchandraen
dc.date.accessioned2015-08-03T09:01:40Zen
dc.date.available2015-08-03T09:01:40Zen
dc.date.issued2011en
dc.identifier.issn15396746en
dc.identifier.doi10.4310/cms.2011.v9.n4.a5en
dc.identifier.urihttp://hdl.handle.net/10754/561659en
dc.description.abstractWe 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.en
dc.publisherInternational Press of Bostonen
dc.titleOn the strong solution of a class of partial differential equations that arise in the pricing of mortgage backed securitiesen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalCommunications in Mathematical Sciencesen
dc.contributor.institutionFederal Home Loan Bank of Atlanta, 1475 Peachtree Street, NE, Atlanta, GA 30309, United Statesen
dc.contributor.institutionCenter for Computational Research, State Universty of New York, Buffalo, NY 14203, United Statesen
dc.contributor.institutionDepartment of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle 517325, Andhra Pradesh, Indiaen
kaust.authorParshad, Ranaen
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