Mortgage Burnout and Selection Effects in Heterogeneous Cox Hazard Models

Paper: arXiv 2603.12422

Authors: 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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework extending Cox hazard models and Ito processes to analyze selection effects and mortgage burnout. However, it is primarily theoretical with limited empirical backtesting or real-world data validation presented in the excerpt.

Research Flowchart

  flowchart TD
    A[Goal: Explain Mortgage Burnout via Heterogeneous Cox Models] --> B[Inputs: Individual Prepayment Hazards & Common Factor Stochasticity]
    B --> C[Formulate Aggregate Hazard Rate as Survival-Weighted Mean]
    C --> D[Apply Ito's Lemma to Extend Deterministic Hazard to Stochastic Setting]
    D --> E[Derive Aggregate Drift Equation with Negative Selection Term]
    E --> F[Key Outcome: Burnout Driven by Cross-Sectional Dispersion & Diffusion]