Weak error approximation for rough and Gaussian mean-reverting stochastic volatility models
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911459429056512 |
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| author | Alfonsi, Aurélien Kebaier, Ahmed |
| author_facet | Alfonsi, Aurélien Kebaier, Ahmed |
| contents | For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using a Euler type scheme with integrated kernels. Our first result is a weak convergence rate for the discretised rough Ornstein-Uhlenbeck process, that is essentially in $\min(3α-1,1)$, where $\frac{t^{α-1}}{Γ(α)} $ is the fractional convolution kernel with $α\in (1/2,1)$. Then, our main result is to obtain the same convergence rate for the corresponding stochastic rough volatility model with polynomial test functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_18234 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weak error approximation for rough and Gaussian mean-reverting stochastic volatility models Alfonsi, Aurélien Kebaier, Ahmed Probability Computational Finance 60H35 60G22 60L90 91G60 For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using a Euler type scheme with integrated kernels. Our first result is a weak convergence rate for the discretised rough Ornstein-Uhlenbeck process, that is essentially in $\min(3α-1,1)$, where $\frac{t^{α-1}}{Γ(α)} $ is the fractional convolution kernel with $α\in (1/2,1)$. Then, our main result is to obtain the same convergence rate for the corresponding stochastic rough volatility model with polynomial test functions. |
| title | Weak error approximation for rough and Gaussian mean-reverting stochastic volatility models |
| topic | Probability Computational Finance 60H35 60G22 60L90 91G60 |
| url | https://arxiv.org/abs/2602.18234 |