Optimal financial resources for Central Counterparties: Introducing default dependence of clearing members: a mixed binomial approach

Abstract

Central counterparties (CCPs) are ˝nancial intermediaries consisting of clearing members trading ˝nancial derivatives between each other. In a ˝nancial network, CCPs become the buyer to every seller and the seller to every buyer. After the 2007-2008 ˝nancial crisis, so called central counterparties have become fundamental ˝nancial institutions worldwide. Nahai-Williamson et al. (2013) develop an expected loss function for clearing members to investigate and ˝nd the optimal quantities of central counterparties ˝nancial resources, i.e. initial margin and default fund, which are safety contributions to the CCP to absorb potential future losses in case of one or several member's defaults. Nahai-Williamson et al. (2013) assume exogenous and independent individual default probabilities, which are uncorrelated with the underlying prices of assets cleared through the CCP. In this thesis, we extend the Nahai-Williamson et al. (2013) model by using a Merton mixed binomial model, which allows for realistic dependencies among default probabilities and lets the prices be correlated with default probabilities themselves. We de˝ne a new expected loss function for clearing members, which is minimized with respect to initial margin and default fund and obtains new optimal quantities for CCP's ˝nancial resources in our extended model. The new framework with default and price dependencies will change the optimal quantities of sources: initial margin and default fund contributions will be di˙erent and higher than previous optimal quantities in Nahai-Williamson et al. (2013). In some cases, our default fund contributions will be 200%, 300% and even 1500% larger than optimal contributions found by Nahai-Williamson et al. (2013). Moreover, the balance between CCP's initial margin and default fund will tend more to the default fund rather than any other ˝nancial source. Although it does not concern optimal ˝nancial resources, we also ˝nd that in the Merton-extended version the expected loss function itself is sometimes 22% and 55% higher than the one de˝ned by Nahai-Williamson et al. (2013) in the same conditions. The economic interpretation of this result is that higher default dependence leads to higher losses, which should be better covered by higher mutualization between clearing members.