Funding and credit risk with locally elliptical portfolio processes: an application to central counterparties

We consider the problem of quantifying credit and funding risks in the presence of initial margin calculated by dynamically updated risk measures such as value-at-risk and expected shortfall. The analytic scaling approach proposed in 2017 by Andersen, Pykhtin and Sokol is generalized from a system driven by Brownian motion to an arbitrary radially symmetric (or “isotropic†) Lévy process, permitting application to models possessing fat-tailed market movements during the margin period of risk. Our mathematical results are applied to derive a closed-form representation of the credit valuation adjustment and of the margin valuation adjustment for centrally cleared portfolios in an arbitrage-free, continuous-time model driven by an isotropic Lévy process. Our results cover the exposures arising from both client clearing and participation in the loss mutualization of clearing member defaults. The latter is a particularly vexing modeling problem due to strong limitations on observable central counterparty (CCP) data. Our model gives rise to a compact valuation expression depending only on a clearing member’s own portfolio, along with certain intuitive macroscopic measures capturing the gross risk and its concentration within the CCP.