Establishing Consistent Collateral Policies for Central Banks’ Open Market Operations

We derive a general framework for collateral risk control determination for central bank's open market operations. This framework allows us to determine the schedule of haircuts consistent with the risk tolerated by the central bank while at the same time reducing the possibility of arbitrage opportunities in sec-ondary markets. Based on the collateral haircuts and predetermined loss level, we derive the probability of incurring a loss higher than allowed (a technique akin to VaR). Accordingly, if the bank fixes its risk exposure, which is related to its risk appetite, the required haircut can be extracted. Default is determined exogenously while marking-to-market is also introduced and margin calls are derived endogenously by the evolution of the underlying used as collateral. A closed form solution is derived for the case of single collateral as well as for port-folios of collaterals when the interest rate is assumed to follow a Vasicek model. In addition to the marking-to-market policy, extensions to the basic framework are presented taking into account time to capture and liquidity sects. We also study the case where there exists correlation between interest rate and the probabilities of default of the counterparty. We consider the portfolio dimen-sion of collateral provisions and its impact on collateral policy. The derivation itself leads to a number of interesting results, notably on the never-documented before portfolio effect of collateralization.