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

Christoph Reisinger; Maria Olympia Tsianni

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arXiv · 2302.00434

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

Christoph Reisinger·Maria Olympia Tsianni

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Abstract

In this paper, we study the Euler--Maruyama scheme for a particle method to approximate the McKean--Vlasov dynamics of calibrated local-stochastic volatility (LSV) models. Given the open question of well-posedness of the original problem, we work with regularised coefficients and prove that under certain assumptions on the inputs, the regularised model is well-posed. Using this result, we prove the strong convergence of the Euler--Maruyama scheme to the particle system with rate 1/2 in the step-size and obtain an explicit dependence of the error on the regularisation parameters. Finally, we implement the particle method for the calibration of a Heston-type LSV model to illustrate the convergence in practice and to investigate how the choice of regularisation parameters affects the accuracy of the calibration.

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Christoph Reisinger, Maria Olympia Tsianni. 2023-02-01. Convergence of the Euler--Maruyama particle scheme for a regularised McKean--Vlasov equation arising from the calibration of local-stochastic volatility models. https://arxiv.org/abs/2302.00434

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