Capital Modeling and Economic Capital for Insurers

Economic Capital Framework

Economic capital is the amount of capital an insurer needs to absorb unexpected losses at a specified confidence level (e.g., 99.5% VaR or 99% TVaR over one year). The calculation requires modeling the full distribution of outcomes across all risk categories: underwriting (reserve and premium risk), market (interest rate, equity, credit spread), credit (reinsurer default), and operational risk. Each risk is modeled separately, then aggregated accounting for diversification. The difference between total standalone capital and diversified capital represents the diversification benefit.

Aggregation Methods

Aggregation approaches include the variance-covariance method (capital = sqrt of sum of rho_{ij}*C_i*C_j)), copula-based simulation (model joint distribution of risk outcomes using a copula), and full internal model simulation (simulate all risks in an integrated stochastic model). The correlation matrix or copula captures dependencies between risks. Stress testing and reverse stress testing complement quantitative models. Capital allocation distributes total capital to business units using methods like the Euler principle (each unit's capital = its marginal contribution to total risk). Exam MAS-II tests capital modeling concepts, aggregation methods, and allocation principles.