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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2504.14343 |
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| _version_ | 1866915251435339776 |
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| author | Reisinger, Christoph Tsianni, Maria Olympia |
| author_facet | Reisinger, Christoph Tsianni, Maria Olympia |
| contents | We analyse a Monte Carlo particle method for the simulation of the calibrated Heston-type local stochastic volatility (H-LSV) model. The common application of a kernel estimator for a conditional expectation in the calibration condition results in a McKean-Vlasov (MV) stochastic differential equation (SDE) with non-standard coefficients. The primary challenges lie in certain mean-field terms in the drift and diffusion coefficients and the $1/2$-Hölder regularity of the diffusion coefficient. We establish the well-posedness of this equation for a fixed but arbitrarily small bandwidth of the kernel estimator. Moreover, we prove a strong propagation of chaos result, ensuring convergence of the particle system under a condition on the Feller ratio and up to a critical time. For the numerical simulation, we employ an Euler-Maruyama scheme for the log-spot process and a full truncation Euler scheme for the CIR volatility process. Under certain conditions on the inputs and the Feller ratio, we prove strong convergence of the Euler-Maruyama scheme with rate $1/2$ in time, up to a logarithmic factor. Numerical experiments illustrate the convergence of the discretisation scheme and validate the propagation of chaos in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical analysis of a particle system for the calibrated Heston-type local stochastic volatility model Reisinger, Christoph Tsianni, Maria Olympia Computational Finance Numerical Analysis We analyse a Monte Carlo particle method for the simulation of the calibrated Heston-type local stochastic volatility (H-LSV) model. The common application of a kernel estimator for a conditional expectation in the calibration condition results in a McKean-Vlasov (MV) stochastic differential equation (SDE) with non-standard coefficients. The primary challenges lie in certain mean-field terms in the drift and diffusion coefficients and the $1/2$-Hölder regularity of the diffusion coefficient. We establish the well-posedness of this equation for a fixed but arbitrarily small bandwidth of the kernel estimator. Moreover, we prove a strong propagation of chaos result, ensuring convergence of the particle system under a condition on the Feller ratio and up to a critical time. For the numerical simulation, we employ an Euler-Maruyama scheme for the log-spot process and a full truncation Euler scheme for the CIR volatility process. Under certain conditions on the inputs and the Feller ratio, we prove strong convergence of the Euler-Maruyama scheme with rate $1/2$ in time, up to a logarithmic factor. Numerical experiments illustrate the convergence of the discretisation scheme and validate the propagation of chaos in practice. |
| title | Numerical analysis of a particle system for the calibrated Heston-type local stochastic volatility model |
| topic | Computational Finance Numerical Analysis |
| url | https://arxiv.org/abs/2504.14343 |