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

Rana Parshad, Derviş Bayazit, Nathaniel S. Barlow, V. Ramchandra Prasad

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)1033-1050
Number of pages18
JournalCommunications in Mathematical Sciences
Volume9
Issue number4
DOIs
StatePublished - 2011

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

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