Mean reversion in stochastic mortality: why and how?
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Mean reversion in stochastic mortality: why and how? Fadoua Zeddouk1 · Pierre Devolder1 Received: 23 October 2019 / Revised: 5 March 2020 / Accepted: 14 May 2020 © EAJ Association 2020
Abstract Life insurance companies use stochastic models to forecast mortality. According to the literature, non-mean reversion models are more suitable for mortality modelling than mean reversion models with a fixed long-term target. In this paper, we adopt stochastic affine processes for the force of mortality and study the impact of adding a time-dependent long-term mean reversion level to two non-mean-reverting processes. We calibrate the models to different generations of the Belgian population and assess these models’ abilities to predict mortality using different statistical methodologies. The backtest shows that the survival curves provided by the mean-reverting processes are closer to reality. Thus, we conclude that incorporating a time-dependent target into these considered models improves their performance significantly. Keywords Stochastic mortality · Mean reversion · Affine process
1 Introduction For life insurance companies and pension funds, mortality risk has been traditionally estimated using a simplified approach to reality, based on deterministic life tables projected from historical mortality rates and added safety margins. While this traditional method may be prudent for risk management, it does not account for uncertainty related to mortality evolution, since a deterministic mortality scenario is applied to risk management and pricing. Ultimately, this approach may lead to a flawed evaluation of life insurance products. Moreover, under the Solvency II Framework Directive, solvency capital must be held to avoid the risk of ruin. This capital is related to the risk of deviation of future mortality based on life expectancy and, therefore, should use stochastic projections. Thus, stochastic models for mortality are needed to measure the trend of improvement in mortality over the next few decades, along with associated uncertainty in the projections. By modelling * Fadoua Zeddouk [email protected] 1
Université Catholique de Louvain, Ottignies‑Louvain‑la‑Neuve, Belgium
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mortality as a stochastic process, reserves can expand to include uncertainty associated with future development of mortality intensity. This method should allow for a more accurate assessment of future commitments that account for the systematic risk of mortality. Moreover, the development of mortality and longevity-related securities requires the use of stochastic models to accurately price financial instruments according to demographic risks. To better predict longevity risk, research and development efforts have recently focused on stochastic mortality models. The Lee–Carter model [12], was the first model to consider increased life expectancy trends in age mortality dynamics and has been used for stochastic forecasts of the U.S. Social Security system and other aspects of the U.S
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