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Probability and Computational Finance Seminar
Zhe Cheng Carnegie Mellon University Title: Mathematical Modeling of an Endogenously Defined Mortgage Rate that Reflects Prepayment Risk Abstract: We consider the problem of identifying endogenous current coupons for To-Be-Announced (TBA) agency mortgage pass through securities. Current coupons play a crucial role in the mortgage industry for pricing and determining the relative value of mortgage backed securities. The current coupon is said to be endogenous if it gives rise to a par valued TBA, taking into account the prepayment risk. Since prepayments both affect the value of the mortgage and depend heavily upon the coupon, the identification of endogenous current coupon involves solving a highly non-trivial fixed point problem.In an intensity based, Markovian model where underlying economic factors affect prepayments, the current coupon is identified as a function of the underlying factors. In order to analyze the fixed point, we perform a perturbation analysis where prepayment intensities are perturbed off of a baseline intensity dependent only upon the factors. We obtain a unique current coupon up to leading orders of the perturbation and show that this approximation does very well in practice. We will prove the existence of endogenous current coupon with nice regularity properties in a model where the intensity does not depend on the initial coupon. And we will propose a method to show the existence of endogenous current coupon in the general case.Time permitting, we will also show how our analysis can be extended to cover defaults and heterogeneous mortgage pools.This is a joint work with Scott Robertson from Carnegie Mellon University. Date: Monday, May 4, 2015 Time: 4:30 pm Location: Wean Hall 8220 Submitted by: Scott Robertson |