The topology of central counterparty clearing networks and network stability

Rui Song, Richard B. Sowers, Jonathan Jones

Research output: Contribution to journalArticlepeer-review

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 maximum-exposure probability is informative and can be used to compare the relative maximum-exposure risks across different network configurations.

Original languageEnglish (US)
Pages (from-to)16-47
Number of pages32
JournalStochastic Models
Volume30
Issue number1
DOIs
StatePublished - Jan 2 2014

Keywords

  • Central counterparty
  • Clearing
  • Large deviations theory
  • Network analysis
  • Systemic risk

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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