Longevity/Mortality Risk Modeling and Securities Pricing

Abstract

Securitization of longevity/mortality risk provides insurers and pension funds an effective, low-cost approach to transferring the longevity/mortality risk from their balance sheets to capital markets. The modeling and forecasting of the mortality rate is the key point in pricing mortality-linked securities that facilitates the emergence of liquid markets. The catastrophic longevity jumps and mortality jumps are significant in historical data and have a critical effect on securities pricing. This paper introduces a stochastic diffusion model with a Double Exponential Jump Diffusion (DEJD) process for mortality time-series, which is the first to capture both asymmetric jump features and cohort effect as the underlying reason for the mortality trend. The DEJD model has the advantage of easy calibration and mathematical tractability. The form of the DEJD model is neat, concise and practical. Compared with previous stochastic models with or without jumps, the DEJD model fits the actual data better. To apply the model, the implied risk premium is calculated based on the Swiss Re mortality bond price. The DEJD model is the first to provide a close-form solution to price the q-forward, which is the standard product contingent on the LifeMetrics index for hedging longevity or mortality risk.