Bayesian forecasting of Prepayment Rates for Individual Pools of Mortgages

This paper proposes a novel approach for modeling prepayment rates of individual pools of mortgages. The model incorporates the empirical evidence that prepayment is past dependent via Bayesian methodology. There are many factors that influence the prepayment behavior and for many of them there is no available (or impossible to gather) information. We implement this issue by creating a Bayesian mixture model and construct a Markov Chain Monte Carlo algorithm to estimate the parameters. We assess the model on a data set from the Bloomberg Database. Our results show that the burnout effect is a significant variable for explaining normal prepayment activities. This result does not hold when prepayment is triggered by non-pool dependent events. We show how to use the new model to compute prices for Mortgage Backed Securities. Monte Carlo simulation is the traditional method for obtaining such prices and the proposed model can be easily incorporated within simulation pricing framework. Prices for standard Pass-Throughs are obtained using simulation.State of Texas Advanced Research Program 003658-0763National Science Foundation CMMI-0457558, DMS-0605102Civil, Architectural, and Environmental Engineerin

Theoretical study of EAS hadronic structure

The structure of extensive air showers (EAS) is determined mainly by the energetic hadrons. They are strongly collimated in the core of the shower and essential difficulties are encountered for resolution of individual hadrons. The properties for resolution are different from the variety of hadron detectors used in EAS experiments. This is the main difficulty in obtaining a general agreement between actually registered data with different detectors. The most plausible source for disagreement is the uncertainty in determination of the energy of individual hadrons. This research demonstrates that a better agreement can be obtained with the average tendency of hadronic measurements if one assumes a larger coefficient of inelasticity and stronger energy increase of the total inelastic cross section in high energy pion interactions. EAS data above 10 to the 5th power GeV are revealing a faster development of hadronic cascades in the air then can be expected by extrapolating the parameters of hadron interactions obtained in accelerator measurements

Imaging instantaneous electron flow with ultrafast resonant x-ray scattering

We propose a novel way to image dynamical properties of nonstationary electron systems using ultrafast resonant x-ray scattering. Employing a rigorous theoretical analysis within the framework of quantum electrodynamics, we demonstrate that a single scattering pattern from a nonstationary electron system encodes the instantaneous interatomic electron current in addition to the structural information usually obtained by resonant x-ray scattering from stationary systems. Thus, inelastic contributions that are indistinguishable from elastic processes induced by a broadband probe pulse, instead of being a concern, serve as an advantage for time-resolved resonant x-ray scattering. Thereby, we propose an approach combining elastic and inelastic resonant x-ray scattering for imaging dynamics of nonstationary electron systems in both real space and real time. In order to illustrate its power, we show how it can be applied to image the electron hole current in an ionized diatomic molecule