Measuring exposure to dependence risk with random Bernstein copula scenarios

This paper considers the problem of measuring the exposure to dependence risk carried by a portfolio with an arbitrary number of two-asset derivative contracts. We develop a worst-case risk measure computed over a set of dependence scenarios within a divergence restricted region. The set of dependence scenarios corresponds to Bernstein copulas obtained by simulating random doubly stochastic matrices. We then devise a method to compute hedging positions when a limited number of hedging instruments are available for trading. In an empirical study, we show how the proposed method can be used to reveal an exposure to dependence risk where usual sensitivity methods fail to reveal it. We also illustrate the ability of the proposed method to generate parsimonious hedging strategies in order to reduce the exposure to dependence risk of a given portfolio.