Inferring dependencies between financial assets with applications to multi-name credit derivatives
In this dissertation we: (1) develop a statistical framework for testing dependence assumptions in a given time series; (2) develop a statistical test for comparing dependence structures (aka copula functions ) derived from the Normal and Student-t distributions and use this to quantify the potential for extreme co-movements and; (3) analyze in detail credit derivative models and their sensitivity to different dependence assumptions. The main results of our studies may be summarized as follows. First, the t-copula assumption is a more plausible model of dependence for the tested time-series; the Normal copula provides a lesser fit than the t-copula but a superior fit compared with the three Archimedean copulas tested, namely, Frank, Gumbel, and Clayton. Second, exploiting the nesting of the Normal copula within the t-family we show that the former can be almost always rejected on the basis of a likelihood ratio test. Third, financial data exhibit a clear tendency for extreme co-movements which cannot be predicted on the basis of a Normal copula model. Fourth, as the dimensionality increases (i.e., the number of assets being tested for dependence increases) the distinction between the Normal and t-copulas become “sharper”. Fifth, the dependence structure of asset returns is strikingly similar to the one underlying equity returns. Finally, the tendency for extreme co-movements does not seem to be affected by the sampling frequency, in contrast to the phenomenon observed in univariate returns that tend to be “heavy-tailed” in higher frequencies, and more “Gaussian-like” in lower frequencies. Our results bear important financial implications which we illustrate throughout this thesis with examples that include: MSCI national equity indices data; risk measure for portfolios of equity options; pricing n th to default baskets; pricing and risk measures of synthetic CDO tranches, and; analysis of portfolio tail dependence indices.