Since November 2012 there is a shortselling ban for sovereign credit default swaps (CDS). The idea is to prevent speculative traders from betting on the default of a country by buying protection without actually being a creditor. Even if the CDS is bought with the intention to protect against losses arising from a sovereign bond position it is forbidden to buy “too much“ CDS protection. The crucial question is: How much CDS nominal is appropriate to compensate for potential losses of a bond position? The present note provides an answer.
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.