On a CCP Model Linking Market Gaps to Defaults

We present a dynamic model of a Central Counterparty (CCP) and use it to quantify the associated credit risks. First, we apply the model to obtain a closed-form approximation to the Credit Valuation Adjustment (CVA) arising due to membership of a CCP; then, we apply the model to economic capital and derive a semi-analytic approximation to the full distribution of losses upto a fixed time horizon. Through a novel mechanism linking margin calls and default times, we investigate the potential wrong-way risk arising due to an extremal margin call triggering the default of a CCP member that holds insufficient capital. We conclude that excessive leverage may increase credit risk to such an extent that a single CCP member clearing an outsized, speculative position may contribute more risk than all the other members combined