The risk of model misspecification and its impact on solvency measurement in the insurance sector

Purpose – The purpose of this paper is to study the risk of misspecifying solvency models for insurance companies. Design/methodology/approach – Based on a basic solvency model, the authors examine the sensitivity of different risk measures with respect to model misspecification. An analysis considers the effects of introducing stochastic jumps and linear, as well as non-linear dependencies into the basic setting on the solvency capital requirements, shortfall probability and expected policyholder deficit. Additionally, the authors take a regulatory view and consider the degree to which the deviations in risk measures, due to the different model specifications, can be diminished by means of requiring interim financial reports. Findings – The simulation results suggest that the sensitivity of solvency capital as a risk measure – as it is in regulatory practice – underestimates the actual misspecification risk that policyholders are exposed to. It is also found that semi-annual mandatory interim reports can already reduce the model uncertainty faced by a regulator, significantly. This has important implications for the design of risk-based capital standards and the implementation of internal solvency models. Originality/value – The results from the Monte Carlo simulation show that changes in the specification of a solvency model have a much greater impact on shortfall probabilities and expected policyholder deficits than they have on capital requirements. The shortfall risk measures react much more sensitively to small changes in the model assumptions, than the capital requirements. This leads us to the conclusion that regulators should not solely rely on capital requirements to monitor the solvency situation of an insurer, but should additionally consider shortfall risk measures. More precisely, an analysis of model risk focusing on the sensitivity of capital requirements will typically underestimate the relevant risk of model misspecification from a policyholder's perspective. Finally, the simulation results suggest that mandatory interim reports on the solvency and financial situation of an insurance company are a powerful tool in order to reduce the model uncertainty faced by regulators.