The estimation of dynamic initial margin (DIM) is a challenging problem. We describe an accurate new approach using Johnson-type distributions, which are fitted to conditional moments, estimated using a least-squares Monte Carlo simulation (the Johnson least-squares Monte Carlo (JLSMC) algorithm). We compare the JLSMC DIM estimates with those computed using an accurate nested Monte Carlo simulation as a benchmark, and with another method that assumes portfolio changes are Gaussian. The comparisons reveal that the JLSMC algorithm is accurate and efficient, producing results that are comparable with nested Monte Carlo with an order of magnitude less computational effort. We provide illustrative examples using the Hull–White and Heston models for different derivatives and portfolios. A further advantage of our new approach is that it relies only on the readily available data that is needed for any exposure or value adjustment calculation.