Applications of copula theory in financial econometrics

The work presented in this dissertation was motivated by the widely accepted observation that many economic variables are non-normally distributed. They exhibit fat-tails, skewness, and recent work suggests that some also exhibit “asymmetric dependence”, where some pairs of variables are more highly correlated during negative movements than positive movements.; This observation raises two important problems: the construction of alternative, more palatable, density specifications, and the description and analysis of dependence between these variables in a more general manner than linear correlation, as when the joint distribution of the variables of interest is non-elliptical the correlation coefficient is no longer sufficient to describe the dependence structure.; The four chapters of this dissertation investigate applications of copula theory to address these problems. The theory of copulas allows us to consider the dependence between two random variables in a general way, and to construct flexible parametric multivariate distributions.; Chapter One extends the existing theory of copulas to allow for conditioning variables, and shows how to construct and evaluate flexible parametric multivariate distributions using copula theory through an application to a model of the joint distribution of the Deutsche mark—U.S. dollar and Japanese yen—U.S. dollar exchange rates.; Chapter Two looks at the multi-stage maximum likelihood estimation of parametric multivariate time series models constructed using copula theory, allowing for the possibility that we have more data available on one variable than another.; Chapter Three provides a link between two findings in the empirical finance literature: those of skewness in individual asset returns and asymmetric dependence between asset returns. I show that the presence of asymmetric dependence between two assets can lead to skewed portfolios even if the individual assets themselves are not skewed.; Chapter Four investigates the importance of skewness and asymmetric dependence for asset allocation in an out-of-sample study. The goal of this chapter was to determine for a particular pair of assets whether flexible density models lead to better portfolio decisions than a multivariate normal distribution model. I find significant improvements, both economically and statistically.