Paper: arXiv 2507.19445

Authors: Kenneth Q. Zhou, Hongjuan Zhou

Abstract

Recent studies have identified long-range dependence as a key feature in the dynamics of both mortality and interest rates. Building on this insight, we develop a novel bi-variate stochastic framework based on mixed fractional Brownian motions to jointly model their long-memory behavior and instantaneous correlation. Analytical solutions are derived under the risk-neutral measure for explicitly pricing zero-coupon bonds and extreme mortality bonds, while capturing the impact of persistent and correlated risk dynamics. We then propose a calibration procedure that sequentially estimates the model and risk premium parameters, including the Hurst parameters and the correlation parameter, using the most recent data on mortality rates, interest rates, and market conditions. Lastly, an extensive numerical analysis is conducted to examine how long-range dependence and mortality-interest correlation influence fair coupon rates, bond payouts and risk measures, providing practical implications for the pricing and risk management of mortality-linked securities in the post-pandemic environment.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical framework using mixed fractional Brownian motion to model excess mortality and interest rates jointly, complete with analytical pricing derivations. It complements this theoretical work with solid empirical calibration using real-world data (HMD and FRED) to analyze post-pandemic risk management applications.

Research Flowchart

  flowchart TD
    A[Goal: Jointly model long-memory dynamics & correlation of mortality & interest rates] --> B[Input Data: Recent mortality rates, interest rates & market conditions]
    B --> C[Framework: Bi-variate Mixed Fractional Brownian Motion]
    C --> D[Calibration: Sequential estimation of Hurst & correlation parameters]
    D --> E[Pricing Engine: Analytical risk-neutral solutions for Zero-Coupon & Extreme Mortality Bonds]
    E --> F[Outcomes: Quantified impact of long-range dependence on fair coupon rates, payouts & risk management]

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0 of 49 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.