Dynamic Initial Margin Estimation Based on Quantiles of Johnson Distributions

The estimation of dynamic initial margin (DIM) for general portfolios is a challenging problem. The present paper describes an accurate new approach, based on regression, that uses Johnson-type distributions, which are fitted to conditional moments estimated using least-squares Monte Carlo simulation (the JLSMC approach). This approach is compared to DIM estimates computed using nested Monte Carlo as a benchmark. Under a number of test cases, the two approaches are shown to be coherent. Furthermore, we show that estimates of DIM produced under the standard regression approach, which assumes portfolio changes are Gaussian, diverges significantly from the better estimates using the JLSMC and nested Monte Carlo approaches. The standard approach performs particularly poorly if the portfolio changes are far from Gaussian (e.g. for options). To further demonstrate the efficacy of the JLSMC approach we provide illustrative examples using Hull-White and Heston models for different derivatives and portfolios. A further advantage of the new approach is that it only relies on the quantities required for any exposure or XVA calculation.