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Mortgage Burnout and Selection Effects in Heterogeneous Cox Hazard Models

Andrew Lesniewski

Abstract

We study the aggregate hazard rate of a heterogeneous population whose individual event intensities are modeled as Cox (doubly stochastic) processes. In the deterministic hazard setting, the observed pool hazard is the survival weighted mean of the individual hazards, and its time derivative equals the mean individual hazard drift minus a variance term. This yields a transparent structural explanation of burnout in mortgage pools. We extend this perspective to stochastic intensity models. The observed pool hazard remains a survival-weighted mean, but now evolves as an Ito process whose drift contains the mean drift of the individual hazards and a negative selection term driven by cross-sectional dispersion, together with a diffusion term inherited from the common factor. We formulate the general identity and discuss special cases relevant to mortgage prepayment modeling.

Mortgage Burnout and Selection Effects in Heterogeneous Cox Hazard Models

Abstract

We study the aggregate hazard rate of a heterogeneous population whose individual event intensities are modeled as Cox (doubly stochastic) processes. In the deterministic hazard setting, the observed pool hazard is the survival weighted mean of the individual hazards, and its time derivative equals the mean individual hazard drift minus a variance term. This yields a transparent structural explanation of burnout in mortgage pools. We extend this perspective to stochastic intensity models. The observed pool hazard remains a survival-weighted mean, but now evolves as an Ito process whose drift contains the mean drift of the individual hazards and a negative selection term driven by cross-sectional dispersion, together with a diffusion term inherited from the common factor. We formulate the general identity and discuss special cases relevant to mortgage prepayment modeling.
Paper Structure (12 sections, 3 theorems, 42 equations)

This paper contains 12 sections, 3 theorems, 42 equations.

Table of Contents

  1. Introduction
  2. Mortgage Pool Heterogeneity
  3. Deterministic Hazards
  4. Stochastic Hazards
  5. Common Factor Hazard Dynamics
  6. Measure Change Interpretation
  7. Frailty Factor Models
  8. Gamma Frailty
  9. Lognormal Frailty
  10. Normal Frailty
  11. Multivariate Frailty
  12. Conclusion

Key Result

Theorem 3.1

Suppose each borrower hazard $\lambda(t,x)$ is differentiable in time. Then the pool hazard satisfies

Theorems & Definitions (5)

  • Definition 2.1
  • Definition 2.2
  • Theorem 3.1
  • Proposition 4.1
  • Proposition 5.1