- Convergence of the Euler — Maruyama particle scheme for a regularised McKean — Vlasov equation arising from the calibration of local-stochastic volatility fashions
Authors: Christoph Reisinger, Maria Olympia Tsianni
Summary: On this paper, we examine the Euler — Maruyama scheme for a particle methodology to approximate the McKean — Vlasov dynamics of calibrated local-stochastic volatility (LSV) fashions. Given the open query of well-posedness of the unique downside, we work with regularised coefficients and show that underneath sure assumptions on the inputs, the regularised mannequin is well-posed. Utilizing this end result, we show the sturdy convergence of the Euler — Maruyama scheme to the particle system with price 1/2 within the step-size and acquire an specific dependence of the error on the regularisation parameters. Lastly, we implement the particle methodology for the calibration of a Heston-type LSV mannequin as an example the convergence in follow and to analyze how the selection of regularisation parameters impacts the accuracy of the calibration
