On the strong solution of a class of partial differential equations that arise in the pricing of mortgage backed securities
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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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.
PublisherInternational Press of Boston