Negative Convexity in Pass-Through MBS: Mechanisms and Conditions

Paper: arXiv 2610.38275

Authors: Kaname Imagawa

Abstract

This paper investigates the mechanisms and conditions underlying negative convexity in pass-through mortgage-backed securities (MBSs) backed by fixed-rate mortgages. We first derive an exact decomposition of MBS prices into three components: the present value of interest-rate-independent cash flows, the present value of principal repaid early through interest-rate-dependent prepayments, and an interest rate option component capturing the reduction in future cash flows due to prepayments. Under a first-order approximation, the latter two components resemble portfolios of floorlets and Asian-style interest rate options, respectively. We then apply a cumulant expansion to derive closed-form valuation approximations under the one-factor Hull–White model. Numerical results show that including the second cumulant improves accuracy relative to a first-cumulant approximation. Building on the price decomposition, we decompose duration and convexity into component-level contributions and express the condition for negative convexity in terms of their second-order interest rate sensitivities. Finally, phase diagrams across interest rate levels and refinancing sensitivities identify the regions where negative convexity occurs and the corresponding sign boundaries. The negative-convexity region expands as the long-run mean of refinancing sensitivity increases. Negative convexity can arise even when no refinancing incentive exists initially, while its magnitude may vary nonmonotonically with the interest rate level. These findings explain negative MBS convexity through the sensitivities of its price components and quantitatively characterize the conditions governing its occurrence.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper demonstrates high mathematical sophistication through its derivations, cumulant expansion, and decomposition of MBS prices and sensitivities. However, it lacks empirical backtesting or extensive data validation, focusing primarily on theoretical and numerical results. The novelty lies in the exact decomposition and the application of cumulant expansion for closed-form approximations.

Research Flowchart

  flowchart TD
    A[Research Goal: Understand Negative Convexity in Pass-Through MBS] --> B{Key Methodology: Price Decomposition & Valuation Model};
    B --> C[Data/Inputs: Fixed-Rate MBS, Interest Rate Levels, Refinancing Sensitivity];
    C --> D{Computational Processes: Cumulant Expansion, Numerical Valuation, Duration/Convexity Decomposition};
    D --> E[Key Findings: Negative convexity arises from component sensitivities; Regions identified via phase diagrams; Magnitude non-monotonic with interest rates; Expands with long-run mean refinancing sensitivity];