THE DETERMINATION OF SOLVENCY CAPITAL REQUIREMENT FOR MARKET RISK OF INSURANCE COMPANY BY COPULA APPROACH

For insurance companies the new conception of legal form of supervision was approved. New directive called Solvency II should be implemented in 2012. The Solvency of insurance companies means an ability to pay liabilities. According this directive the insurance companies have to determine the solvency capital requirements for given risks. From the point of view of supervisor bodies, the level of solvency of insurance companies is given by a Solvency II concept (compare to Basel II for banks). A novel approach of Solvency II is to take into account also market, credit, and operational risk, while two distinct requirements, the Minimum Capital Requirement (MCR) and the Solvency Capital Requirement (SCR) are distinguished In this paper, we estimate both requirements for an internationally diversified equity portfolio of an insurance company. In order to model the portfolio evolution, multidimensional Levy models coupled together by elliptical ordinary copula functions are assumed. We observe that elliptical (ie. symmetric) copula functions fail substantially in risk estimation over five day horizon. It results into 10% to 15% error in the estimation of the overall capital requirement.