Resolving a clearing member’s default a Radner equilibrium approach

For vanilla derivatives, which form the core of investment banks’ hedging portfolios, central clearing via central counterparties (CCPs) has become the prevailing standard. A fundamental role of a CCP is to ensure an efficient and effective resolution process in the event of a clearing member’s default. Upon such a default, the CCP is tasked with hedging and subsequently auctioning or liquidating the defaulted positions. While the counterparty credit risk associated with auctioning has been examined in prior studies from a valuation adjustments (XVA) perspective, this work focuses on evaluating the costs associated with hedging or liquidation. This is achieved by contrasting pre- and post-default market equilibria through a Radner equilibrium framework applied to portfolio allocation and price discovery in both scenarios. We establish the unique existence of Radner equilibria and provide both analytical and numerical solutions within elliptically distributed market settings. These insights equip CCPs with a rational basis for determining whether to hedge, auction, or liquidate defaulted portfolios in specific markets. Moreover, clearing members can leverage these findings to conduct what-if analyses, addressing inquiries from senior management and regulatory bodies. This study also underscores the advantages of central clearing over bilateral trading from a default resolution perspective.