Longevity risk in Solvency II: Standard formula and internal model compared

  • Fang Qi Wu Fang Qi Wu

Two methods to determine the Solvency Capital Requirement (SCR) for longevity risk as described by the Solvency II Directive are compared: the Solvency II standard approach and an internal model based on the stochastic Lee-Carter mortality model. The Lee-Carter (1992) model is used to estimate and forecast future mortality for Dutch gender-specific data. Forecasts from this model are used to simulate portfolio participants’ lifetimes to determine the SCR with the 99.5% VaR. The standard approach uses a one-off shock for the best estimate one-year mortality rates as a simplification for the 99.5% Value-at-Risk of the internal model, both in excess of the best estimate value of the liabilities for sample pension portfolios. The results indicate that, in case investment risk is hedged and interest rate risk has been accounted for, the internal model proposed in this thesis consistently gives lower SCRs than the standard approach. Although the SCRs’ size depends on portfolio composition and factors such as the estimation period, this may be a reason for insurers to choose to develop an internal model rather than using the standard approach. However, one should be reminded that the Lee-Carter model used here only takes into account trend risk, while disregarding level, model and parameter risk. The uncertainty with respect to portfolio-specific mortality is found to be of significant influence to the results, although its impact still seems smaller than the shock proposed by Solvency II. This result falls in line with the insurance field arguing that the 20% shock size is too large.

Netspar, Network for Studies on Pensions, Aging and Retirement, is a thinktank and knowledge network. Netspar is dedicated to promoting a wider understanding of the economic and social implications of pensions, aging and retirement in the Netherlands and Europe.


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