• Dependence and Risk Management

    The maximal probability of a joint default under given marginals

    Starting from given univariate survival functions, the so-called Dobrushin Theorem can be applied to identify the dependence structure that maximizes the probability of a joint default. For inhomogeneous marginals, the solution is not represented by the comonotonicity copula, opposed to a common modeling (mal-)practice in the financial industry. Moreover, a stochastic model that respects the marginal laws and attains the upper bound for joint defaults can be costructed. To illustrate the theory, we bootstrap default probabilities from credit default swap contracts referencing on EU peripherals and Germany and compute the upper bound for the probability of Germany defaulting jointly with one of the peripherals.