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.

[1]  C. Robert,et al.  Estimating Mixtures of Regressions , 2003 .

[2]  Chester Spatt,et al.  The Effect of Refinancing Costs and Market Imperfections on the Optimal Call Strategy and the Pricing of Debt Contracts , 2005 .

[3]  Richard Roll,et al.  Prepayments on fixed-rate mortgage-backed securities , 1989 .

[4]  Richard Stanton.  Rational Prepayment and the Valuation of Mortgage-Backed Securities , 1995 .

[5]  Richard Stanton.  Forthcoming: Journal of Real Estate Finance and Economics Unobservable Heterogeneity and Rational Learning: Pool Specific vs. Generic Mortgage-Backed Security Prices , 1997 .

[6]  Adrian F. M. Smith,et al.  Gibbs Sampling for Marginal Posterior Expectations , 1991 .

[7]  N. Wallace,et al.  An Empirical Test of a Two-Factor Mortgage Valuation Model: How Much Do House Prices Matter? , 2003 .

[8]  John J. McConnell,et al.  Valuation of GNMA Mortgage-Backed Securities , 1981 .

[9]  S. Chib,et al.  Bayesian analysis of binary and polychotomous response data , 1993 .

[10]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[11]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[12]  A. Zellner.  Optimal Information Processing and Bayes's Theorem , 1988 .

[13]  C. Robert,et al.  A Mixture Approach to Bayesian Goodness of Fit , 2002 .

[14]  Lihong Yang,et al.  Spatial Heterogeneity in Mortgage Terminations by Refinance, Sale and Default , 2003 .

[15]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[16]  S. Ross,et al.  A theory of the term structure of interest rates'', Econometrica 53, 385-407 , 1985 .

[17]  Eduardo S. Schwartz,et al.  Prepayment and the Valuation of Mortgage-Backed Securities , 1989 .

[18]  C. Robert,et al.  Estimation of Finite Mixture Distributions Through Bayesian Sampling , 1994 .

[19]  J. Quigley,et al.  Woodhead Behavior and the Pricing of Residential Mortgages , 2004 .

[20]  B. Silverman,et al.  Using Kernel Density Estimates to Investigate Multimodality , 1981 .

[21]  Suresh M. Sundaresan,et al.  Fixed Income Markets and Their Derivatives , 1996 .