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In this paper, we study the Euler--Maruyama scheme for a particle method toapproximate the McKean--Vlasov dynamics of calibrated local-stochasticvolatility (LSV) models. Given the open question of well-posedness of theoriginal problem, we work with regularised coefficients and prove that undercertain assumptions on the inputs, the regularised model is well-posed. Usingthis result, we prove the strong convergence of the Euler--Maruyama scheme tothe particle system with rate 1/2 in the step-size and obtain an explicitdependence of the error on the regularisation parameters. Finally, we implementthe particle method for the calibration of a Heston-type LSV model toillustrate the convergence in practice and to investigate how the choice ofregularisation parameters affects the accuracy of the calibration.

Convergence of the Euler--Maruyama particle scheme for a regularised  McKean--Vlasov equation arising from the calibration of local-stochastic  volatility models