The Market Value Margin Within The Distribution-Free Chain Ladder Model -A Way To Account For Calendar Year Effects And Aggregating Lines Of Business

Under European and Swiss solvency directives, general insurance companies have to calculate a market value margin (aka risk margin or MVM) for the prediction uncertainty of reserves over each accounting year and until the end of the runoff. The prediction uncertainty is generally split into a process error and an estimation error. In the distribution-free chain ladder framework, [10] derived analytical formulas for the prediction uncertainty over accounting years and showed that they add up to the total runoff uncertainty as given by the Mack error. We suggest a way to modify their methodology in order to account for calendar year uncertainties like a legal reform. Further, we derive the minimum and the maximum market value margin that can result with our modification, which is useful to quantify model uncertainty. Besides, we highlight the simplifications and omissions of the presented ways to infer the MVM. Finally, we discuss aggregating different lines of business. The presented formulas can be calculated in a spreadsheet.

Keywords: Market value margin, distribution-free chain ladder model, reserving risk, calendar year effects, SST, Solvency II