Modeling excess mortality and interest rates using mixed fractional Brownian motions

Abstract Recent studies have identified long-range dependence (LRD) as a key feature in the dynamics of both mortality and interest rates. Building on this insight, we develop a novel bivariate stochastic framework based on mixed fractional Brownian motions to jointly model their long-memory behavior and instantaneous correlation. Analytical solutions are derived under the pricing measure for explicitly valuing zero-coupon bonds and pricing 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 LRD 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.