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2024 | OriginalPaper | Chapter

Convergence of the Euler–Maruyama Particle Scheme for a Regularised McKean–Vlasov Equation Arising from the Calibration of Local-Stochastic Volatility Models

Authors : Christoph Reisinger, Maria Olympia Tsianni

Published in: Monte Carlo and Quasi-Monte Carlo Methods

Publisher: Springer International Publishing

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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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Title: Convergence of the Euler–Maruyama Particle Scheme for a Regularised McKean–Vlasov Equation Arising from the Calibration of Local-Stochastic Volatility Models
Authors: Christoph Reisinger
Maria Olympia Tsianni
Publisher: Springer International Publishing
Book: Monte Carlo and Quasi-Monte Carlo Methods
Print ISBN: 978-3-031-59761-9

Electronic ISBN: 978-3-031-59762-6

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-59762-6_28

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