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Deterministic shock vs. stochastic value-at-risk – an analysis of the Solvency II standard model approach to longevity risk. (English) Zbl 1232.91341
Summary: In general, the capital requirement under Solvency II is determined as the 99.5% value-at-risk of the available capital. In the standard model’s longevity risk module, this value-at-risk is approximated by the change in net asset value due to a pre-specified longevity shock which assumes a 25% reduction of mortality rates for all ages. We analyze the adequacy of this shock by comparing the resulting capital requirement to the value-at-risk based on a stochastic mortality model. This comparison reveals structural shortcomings of the 25% shock and therefore, we propose a modified longevity shock for the Solvency II standard model. We also discuss the properties of different risk margin approximations and find that they can yield significantly different values. Moreover, we explain how the risk margin may relate to market prices for longevity risk and, based on this relation, we comment on the calibration of the cost of capital rate and make inferences on prices for longevity derivatives.

MSC:
91B30 Risk theory, insurance (MSC2010)
91G50 Corporate finance (dividends, real options, etc.)
Software:
Human Mortality
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