The impact of time discretization on solvency measurement

The purpose of this paper is to study how the discretization interval affects the solvency measurement of a property-liability insurance company.

Starting with a basic solvency model, the authors study the impact of the discretization interval on risk measures. The analysis considers the sensitivity of the discrepancy between the risk measures in continuous and discrete time to various parameters, such as the asset-to-liability ratio, the characteristics of the asset and liability processes, as well as the correlation between assets and liabilities. Capital requirements for the one-year planning horizon in continuous vs discrete time are reported as well. The purpose is to report the degree to which the deviations in risk measures, due to the different discretization intervals, can be reduced by means of increasing the frequency with which the risk measures are assessed.

The simulation results suggest that the risk measures of an insurance company are consistently underestimated when assessed on an annual basis (as it is currently done under insurance regulation such as Solvency II). The authors complement the analysis with the capital requirements of an insurance company and conclude that more frequent discretization translates into higher capital requirements for the insurance company. Both the probability of ruin and the expected policyholder deficit (EPD) can be reduced through intermediate financial reports.

The results from our simulation analysis suggest that that the choice of discretization interval has an impact on the risk assessment of an insurance company which uses the probability of ruin and the EPD as risk measures. By assessing the risk measures once a year, both risk measures and the capital requirements are consistently underestimated. Therefore, the recommendation for risk managers is to complement the capital requirements in solvency regulation with sensitivity analyses of the risk measures presented with respect to time discretization. On the one hand, it seems to us that there is value in knowing about the substantial discrepancy between the focused time discrete ruin probability and EPD compared to the continuous version. On the other hand, and if there are no substantial transaction costs associated with more frequent monitoring of solvency figures, a frequent update would be helpful to increase the accuracy of the calculations and reduce the EPD.