Modeling Excess Mortality and Interest Rates using Mixed Fractional Brownian Motions

TL;DR

This paper introduces a new bi-variate stochastic model using mixed fractional Brownian motions to jointly capture long-range dependence and correlation in mortality and interest rates, with applications to pricing mortality-linked securities.

Contribution

It develops an analytical framework for modeling and pricing mortality and interest rate dynamics with long-memory and correlation, including a calibration method using recent data.

Findings

Long-range dependence significantly affects bond pricing.

Correlation impacts risk measures and coupon rates.

Model provides practical tools for mortality-linked security valuation.

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.