The riskiness of longevity indexed life annuities in a stochastic Solvency II perspective

This paper investigates the problem of quantifying the impact of unex- pected deviations of mortality trend on a longevity indexed life annuity in a Solvency II perspective. Solvency II quantitative requirements regulate the margins required to offset the insurance risk in a one year risk horizon. Indeed, the idea of deepening the expected changes of future mortality rates over a single year is gaining. In the following the authors propose a com- putational tractable approach to assess the technical provisions by means of an internal model, in line with Solvency II directives. The impact of adverse effects of the mortality dynamics is investigated. Mortality is modelled by means of a stochastic CIR type model; an ex post analysis is proposed relying on Italian mortality data.