  A clearing member of a Central Counterparty (CCP) is exposed to losses on
their default fund and initial margin contributions. Such losses can be
incurred whenever the CCP has insufficient funds to unwind the portfolio of a
defaulting clearing member. This does not necessarily require the default of
the CCP itself. In this note we aim to quantify the risk a financial
institution has when facing a CCP.
  We show that a clearing member's CCP risk is given by a sum of exposures to
each of the other clearing members. This arises because of the implicit default
insurance that each member has provided in the form of mutualised, loss sharing
collateral. We calculate the exposures by explicitly modeling the capital
structure of a CCP as well as the loss distributions of the individual member
portfolios.
  An important consideration in designing the model is the limited transparency
with respect to the portfolio composition and collateral levels of individual
clearing members. To overcome this we leverage the fact that, for a typical
CCP, margin levels are risk-based. In particular, we parameterise the portfolio
loss tail as a Pareto distribution and we calibrate this to the CCP defined
probability of losses exceeding the posted initial margin levels.
  A key aspect of the model is that we explicitly take into account wrong-way
risk, i.e. the fact that member defaults are more likely to occur in stressed
market conditions, as well as potential contagion between a member's default
and the losses on his portfolio.
