Regulatory correlation matrix
The table of coefficients set by the Solvency II delegated regulation for aggregating SCR modules and submodules. It alone produces the standard formula's diversification benefit.
Annex IV of Directive 2009/138/EC of November 25, 2009: the modules of the basic SCR are aggregated through a square root of a double sum, weighted by correlation coefficients set in advance. Delegated Regulation (EU) 2015/35, applicable since January 1, 2016, does the same inside the modules. The undertaking estimates nothing, and a Maltese insurer applies the same matrix as a German group. A monoline company gets no diversification across modules, while a composite group gets a great deal, which explains part of the sector's consolidation. The coefficients are conservative and sometimes asymmetric: in the market module, the correlation between interest rate and equity risk depends on the direction of the rate shock. When the risk profile departs significantly from these assumptions, the open route is an undertaking specific parameter on certain submodules, or a partial internal model. Quietly adjusting a coefficient is not on the list.
Delegated Regulation (EU) 2015/35, applicable from January 1, 2016 alongside Solvency II. At the level of the basic SCR (Annex IV of Directive 2009/138/EC), the correlation coefficient between market risk and non-life underwriting risk is set at 0.25; between non-life and health underwriting, it is zero. Take an insurer whose market module comes to 420M EUR and non-life module to 180M EUR. Aggregation gives the square root of (420² + 180² + 2 × 0.25 × 420 × 180), about 497M EUR, against 600M EUR on a straight sum.
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