Initial margin with risky collateral

The provision of initial margin (IM) for noncentrally cleared derivatives has gained prominence in financial markets as a way to mitigate counterparty credit risk. IM pro- tects transacting parties from the potential increase in future exposure that could arise from the portfolio value change during the time that it takes to close out and replace the portfolio following a counterparty default. The Basel Committee on Banking Supervision prescribes IM as the ten-day value-at-risk (VaR) of the portfolio at the 99th percentile confidence level. Current industry standard VaR approaches such as parametric or historical VaR methods necessitate an assumption that IM is posted in cash or cash-equivalent assets. Although many counterparty-credit-risk-related models exist in the academic literature, there has been little focus on achieving a theoretical basis for calculating margin with consideration of market risk of the collateral. In this paper, we explore the complication of calculating the IM amount required when collateral comprises risky assets in a parametric VaR framework. We show that the required IM amount can be calculated by solving a quadratic inequality. We also introduce a geometric structure to compare the IM amounts calculated using risky and nonrisky collateral.