Stochastic portfolio specific mortality and the quantification of mortality basis risk

The last decennium a vast literature on stochastic mortality models has been developed.However, these models are often not directly applicable to insurance portfolios because:a) For insurers and pension funds it is more relevant to model mortality rates measured in insured amounts instead of measured in number of policies.b) Often there is not enough insurance portfolio specific mortality data available to fit such stochastic mortality models reliably.In practice, these issues are often solved by applying a (deterministic) portfolio experience factor to projected (stochastic) mortality rates of the whole country population. This factor isusually based on historical portfolio mortality rates, measured in amounts. However, it is reasonable to assume that this portfolio experience factor is also a stochastic variable.Therefore, in this paper a stochastic model is proposed for portfolio mortality experience.Adding this stochastic process to a stochastic country population mortality process leads to stochastic portfolio specific mortality rates, measured in insured amounts. The proposed stochastic process is applied to two insurance portfolios, and the impact on the Value at Risk for longevity risk is quantified. Furthermore, the model can be used to quantify the basis risk that remains when hedging portfolio specific mortality risk with instruments of which thepayoff depends on population mortality rates. The conclusion is that adding this stochastic process can have a significant impact on the Value at Risk of an insurance portfolio and the hedge efficiency of a possible hedge, depending on the size of this portfolio.