Copulas: Dependence Modeling

This lecture covers copulas, which model the dependence between random variables by isolating the dependence structure. It explains the properties of copulas, such as being increasing in each component and satisfying the rectangle inequality. Sklar's Theorem is discussed, showing the relationship between copulas and joint distributions. The lecture also delves into different types of copulas, including the independence, comonotonicity, and countermonotonicity copulas. Examples, such as the Gaussian copula, are provided to illustrate these concepts. The lecture concludes with the simulation of copulas and meta distributions, emphasizing the practical applications of copulas in risk management.