Volume 31, Issue 1 - Special Issue: Systemic Risk / Benjamin Jourdain and Agnès Sulem

We study the impact of central clearing of over-the-counter (OTC) transactions on counterparty exposures in a market with OTC transactions across several asset classes with heterogeneous characteristics. The impact of introducing a central counterparty (CCP) on expected interdealer exposure is determined by the tradeoff between multilateral netting across dealers on one hand and bilateral netting across asset classes on the other hand. We find this tradeoff to be sensitive to assumptions on heterogeneity of asset classes in terms of `riskyness' of the asset class as well as correlation of exposures across asset classes. In particular, while an analysis assuming independent, homogeneous exposures suggests that central clearing is efficient only if one has an unrealistically high number of participants, the opposite conclusion is reached if differences in riskyness and correlation across asset classes are realistically taken into account. We argue that empirically plausible specifications of model parameters lead to the conclusion that central clearing does reduce interdealer exposures: the gain from multilateral netting in a CCP overweighs the loss of netting across asset classes in bilateral netting agreements. When a CCP exists for interest rate derivatives, adding a CCP for credit derivatives is shown to decrease overall exposures. These findings are shown to be robust to the statistical assumptions of the model as well as the choice of risk measure used to quantify exposures.

We study a preferred equity infusion government program set to mitigate interbank contagion. Financial institutions are prone to insolvency risk channeled through the network of interbank debt and to funding liquidity risk. The government seeks to maximize, under budget constraints, the total net worth of the financial system or, equivalently, to minimize the dead-weight losses induced by bank runs. The government is assumed to have complete information on interbank debt. The problem of quantifying the optimal amount of infusions can be expressed as a convex combinatorial optimization problem, tractable when the set of banks eligible for intervention (core banks) is sufficiently, yet realistically, small. We find that no bank has an incentive to withdraw from the program, when the preferred dividend rate paid to the government is equal to the government's outside return on the intervention budget. On the other hand, it may be optimal for the government to make infusions in a strict subset of core banks.

This paper is dedicated to the consistency of systemic risk measures with respect to stochastic dependence. It compares two alternative notions of Conditional Value-at-Risk (CoVaR) available in the current literature. These notions are both based on the conditional distribution of a random variable Y given a stress event for a random variable X , but they use different types of stress events. We derive representations of these alternative CoVaR notions in terms of copulas, study their general dependence consistency and compare their performance in several stochastic models. Our central finding is that conditioning on X  ≥ VaR α ( X ) gives a much better response to dependence between X and Y than conditioning on X  = VaR α ( X ). We prove general results that relate the dependence consistency of CoVaR using conditioning on X  ≥ VaR α ( X ) to well established results on concordance ordering of multivariate distributions or their copulas. These results also apply to some other systemic risk measures, such as the Marginal Expected Shortfall (MES) and the Systemic Impact Index (SII). We provide counterexamples showing that CoVaR based on the stress event X  = VaR α ( X ) is not dependence consistent. In particular, if ( X ,  Y ) is bivariate normal, then CoVaR based on X  = VaR α ( X ) is not an increasing function of the correlation parameter. Similar issues arise in the bivariate t model and in the model with t margins and a Gumbel copula. In all these cases, CoVaR based on X  ≥ VaR α ( X ) is an increasing function of the dependence parameter.

We consider convex risk measures in a spatial setting, where the outcome of a financial position depends on the states at different nodes of a network. In analogy to the theory of Gibbs measures in Statistical Mechanics, we discuss the local specification of a global risk measure in terms of conditional local risk measures for the single nodes of the network, given their environment. Under a condition of local law invariance, we show that a consistent local specification must be of entropic form. Even in that case, a global risk measure may not be uniquely determined by the local specification, and this can be seen as a source of “systemic risk”, in analogy to the appearance of phase transitions in the theory of Gibbs measures

In the conditional setting we provide a complete duality between quasiconvex risk measures defined on L 0 modules of the L p type and the appropriate class of dual functions. This is based on a general result which extends the usual Penot-Volle representation for quasiconvex real valued maps.