A Note on Tail Dependence Regression

In financial practice, it is important to understand the dependence structure between the returns of individual assets and the market index. This particularly true under extreme situations. Theoretically, this amounts to regress the dependence relationship against a set of pre-specified predictive variables. To this end, we propose here a novel method called tail dependence regression. It assumes a tail dependence index model between individual assets and market index. Subsequently, such a tail dependence index is modeled as a linear combination of the predictors through a monotonic transformation. An approximate maximum likelihood method is then developed to estimate the unknown regression coefficients. The resulting estimator's asymptotic properties are investigated theoretically. Numerical studies including both simulated and real datasets are presented for illustration purpose