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Title: A stochastic partial differential equation approach to mortgage backed securities
Author: Ahmad, Ferhana
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2012
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The market for mortgage backed securities (MBS) was active and fast growing from the issuance of the first MBS in 1981. This enabled financial firms to transform risky individual mortgages into liquid and tradable market instruments. The subprime mortgage crisis of 2007 shows the need for a better understanding and development of mathematical models for these securities. The aim of this thesis is to develop a model for MBS that is flexible enough to capture both regular and subprime MBS. The thesis considers two models, one for a single mortgage in an intensity based framework and the second for mortgage backed securities using a stochastic partial differential equation approach. In the model for a single mortgage, we capture the prepayment and default incentives of the borrower using intensity processes. Using the minimum of the two intensity processes, we develop a nonlinear equation for the mortgage rate and solve it numerically and present some case studies. In modelling of an MBS in a structural framework using stochastic PDEs (SPDEs), we consider a large number of individuals in a mortgage pool and assume that the wealth of each individual follows a stochastic process, driven by two Brownian mo- tions, one capturing the idiosyncratic noise of each individual and the second a common market factor. By defining the empirical measure of a large pool of these individuals we study the evolution of the limit empirical measure and derive an SPDE for the evolution of the density of the limit empirical measure. We numerically solve the SPDE to demonstrate its flexibility in different market environments. The calibration of the model to financial data is the focus of the final part of thesis. We discuss the different parameters and demonstrate how many can be fitted to observed data. Finally, for the key model parameters, we present a strategy to estimate them given observations of the loss function and use this to determine implied model parameters of ABX.HE.
Supervisor: Hambly, Ben Sponsor: Higher Education Commission, Government of Pakistan
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics ; Mathematical finance ; finance ; stochastic PDEs