Volterra Mortality Model: Actuarial Valuation and Risk Management with Long-Range Dependence

Abstract

While abundant empirical studies support the long-range dependence (LRD) of mortality rates, the corresponding impact on mortality securities are largely unknown due to the lack of appropriate tractable models for valuation and risk management purposes. We propose a novel class of Volterra mortality models that incorporate LRD into the actuarial valuation, retain tractability and are consistent with the existing continuous-time affine mortality models. We derive the survival probability in closed-form solution by taking into account of the historical health records. The flexibility and tractability of the models make them useful in valuing mortality-related products such as death benefit, annuity, longevity bond and many others as well as offering optimal mean-variance mortality hedging rules. Numerical studies are conducted to examine the impact of LRD within mortality rates on various insurance products and the hedging efficiency.