Vine copulas for capital requirements: a probability equivalent level analysis

The study of capital requirements is an extremely important topic for the stability of the financial system. Recent geopolitical shocks including the war in Ukraine, the Israeli-Palestinian conflict, tensions on supply chains in the Red Sea, in parallel with the Quantitative Tightening monetary policies of central banks are putting its robustness under pressure. Being able to give an estimate of risk and interdependencies within investment portfolios allows one to have a clear vision of costs-benefits in terms of risk-rewards. This work proposes the use of copula theory both to address the problem of studying assets dependencies and predicting capital requirements in the form of risk measures. The class of Vine copulas is presented, which aims to overcome the limits linked to the adoption of a particular family of copulas in addressing the cited topics. This class in fact allows modeling the problem without the need to rely on a precise family but incorporating them all, within the computational limits of the R package used. A Monte Carlo simulation is developed and the validity of presented models is confirmed. Finally, an analysis of probability equivalent levels is carried out, a tool that could be very useful for risk management, since it enables the comparison of risk measures under different conditions of observability of financial markets.