The Topology of Central Counterparty Clearing Networks and Network Stability

Abstract

This paper derives a measure of central counterparty (CCP) clearing-network risk that is based on the probability that the maximum exposure (the N-th order statistic) of a CCP to an individual general clearing member is large. Our analytical derivation of this probability uses the theory of Laplace asymptotics, which is related to the large deviations theory of rare events. The theory of Laplace asymptotics is an area of applied probability that studies the exponential decay rate of certain probabilities and is often used in the analysis of the tails of probability distributions. We show that the maximum-exposure probability depends on the topology, or structure, of the clearing network. We also derive a CCP's Maximum-Exposure-at-Risk, which provides a metric for evaluating the adequacy of the CCP's and general clearing members' loss-absorbing financial resources during rare but plausible market conditions. Based on our analysis, we provide insight into how clearing-network structure can affect the maximum-exposure risk of a CCP and, thereby, network stability. We show that the rate function (the exponential decay rate) of the maximumexposure probability is informative and can be used to compare the relative maximum-exposure risks across different network configurations.

Does Central Clearing Reduce Counterparty Risk in Realistic Financial Networks?

“…Jackson and Manning examine the impact using a range of metrics, while Galbiati and Soramäki focus on the impact on exposures measured as averages over time, or across direct counterparties, in terms of a single asset class. Song, Sowers and Jones (2014) extend the Galbiati and Soramäki framework to study the effect of network structure on the maximum exposure risk of the CCP itself, and use extreme value theory to obtain analytical results.…”

Centralized netting in financial networks

“…Jackson and Manning (2007) and Galbiati and Soramäki (2012) use different approaches to examine the desirability of tiering -that is, restricting direct access to the CCP to a limited set of counterparties. Song, Sowers, and Jones (2014) extend the Galbiati and Soramäki framework to study the effect of network structure on the maximum exposure risk of the CCP itself, and use extreme value theory to obtain analytical results.…”