Analyzing and modeling multivariate association

Meer over het boek

Many applications in quantitative finance, such as estimating the Value-at-Risk of a portfolio, require modeling dependencies among numerous random variables. The common approach is Pearson’s correlation coefficient, which relies on covariance and captures only linear dependencies. This method is effective only for certain distributions, like the multivariate normal distribution, which fails to fully characterize dependence structures in many empirical datasets, especially those that are non-normal and exhibit asymmetric patterns. For instance, the multivariate normal distribution often underestimates the likelihood of simultaneous extremes, leading to inaccurate risk assessments. Consequently, it is often unsuitable for practical applications. In response, the theory of copulas has gained significant attention as an alternative for dependence modeling. The author introduces a new class of measures of association between random vectors that remain invariant to the marginal distribution functions and can differentiate between positive and negative associations. The second part of the work addresses high-dimensional dependencies using Pair-copula constructions, presenting a data-driven sequential estimation method for these models. Empirical applications demonstrate their effectiveness in Value-at-Risk forecasting and spatial modeling of meteorological data.