Estimation of Future Initial Margins in a Multi-Curve Interest Rate Framework

We propose an approach for the dynamical estimation of initial margins. We determine initial margins at future points in time by computing a risk measure of the modelled price increment over a margin period of risk. As an example, we produce the initial margin process for interest rate swap clearing where we assume that the swap price process is driven by a two-factor multi-curve interest rate model that exhibits good calibration properties. The obtained initial margin dynamics incorporate "forward-looking" information present in swaptions market data to which the swap price model is calibrated. We compare the model-generated initial margin process to initial margin data provided by clearing houses and propose adjustments to reduce the observed gap. In doing so, we in effect calibrate the initial margin process to additional market information possibly present in historical market data but not captured in the swaptions market. The margin valuation adjustment (MVA) process is obtained by an application of the risk-neutral valuation formula where the initial margin process is taken as the underlying instrument. We conclude with answers to questions we have received from the financial industry