InsurAce's capital model refers to the EIOPA's Solvency II, the prudential regime for insurance and reinsurance undertakings in the EU. It sets out requirements applicable to insurance and reinsurance companies to ensure the adequate protection of policyholders and beneficiaries.
At the core of the new regulatory framework, Solvency II is an economic risk-based approach that should assess the "overall solvency" of insurance and reinsurance undertakings through quantitative and qualitative measures. Under Solvency II, the undertakings' solvency requirements are determined based on their risk profiles and how such risks are managed, providing the right incentives for sound risk management practices and securing enhanced transparency.
There are different tiers of capital requirements under Solvency II, among which the Solvency Capital Requirement (SCR) and Minimum Capital Requirement (MCR) are the two critical criteria. The SCR is the capital required to ensure that the insurance company will be able to meet its obligations over the next 12 months with a probability of at least 99.5%, where MCR represents the threshold to correspond to an 85% probability of adequacy over 12 months and is bounded between 25% and 45% of the SCR. For supervisory purposes, the SCR and MCR can be regarded as "soft" and "hard" floors.
Mathematically, is made up of
The first item is the discounted best estimate of all future cash flows, namely, the expected claim losses and other expenses minus future premiums receivable. In our case, the discounted best estimate for a portfolio will be equal to
Then, the overall can be formulated as follows, which is to cover the whole underwriting
where is correlations between each pair of Contracts.
The additional funds are reserved for the loss caused by "long tail" losses, which is calculated as follows
where is the risk factor to scale the capital and is the Cover Amounts for individual portfolio i.