Communications in Mathematical Sciences
Volume 9 (2011)
On the strong solution of a class of partial differential equations that arise in the pricing of mortgage backed securities
Pages: 1033 – 1050
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.
mortgage backed security, reduced modeling, mild solution, strong solution, Fourier spectral method
2010 Mathematics Subject Classification
35A01, 35D35, 76M22, 91G20, 91G80