Capital modelling, solvency and regulation
This domain tests regulatory and economic capital, risk aggregation, diversification, model validation and the use of capital models in decision-making.
Capital concepts
Regulatory capital is the minimum required by IRDAI; economic capital is the amount needed to meet a chosen confidence level over a horizon. Risks include insurance, market, credit, operational and liquidity risk. Standalone capital figures are aggregated using a dependence structure, often a correlation matrix or copula. Diversification benefit is the difference between the sum of standalone capitals and the aggregated capital. Models support ORSA, reinsurance optimisation, business planning and capital allocation.
Worked example
Two risks have standalone 99.5% VaR capitals of INR 100 crore and INR 80 crore, with correlation 0.3. Using a variance-covariance aggregation: variance = 100^2 + 80^2 + 2 x 0.3 x 100 x 80 = 10,000 + 6,400 + 4,800 = 21,200. Aggregated capital = square root of 21,200 = INR 145.6 crore. The sum of standalone capitals is INR 180 crore, so the diversification benefit is INR 34.4 crore. This assumes elliptical dependence and normal-like tails.
Traps
Adding standalone capitals ignores diversification but can be conservative. Assuming independence understates tail dependence. Model validation must include backtesting and sensitivity testing. Do not use regulatory formula output as economic capital without adjustment. Reinsurance relief must be tested for actual risk transfer.