We present weak approximations schemes of any order for the Heston model that are obtained by using the method developed by Alfonsi and Bally (2021). This method consists in combining approximation schemes calculated on different random grids to increase the order of convergence. We apply this method with either the Ninomiya-Victoir scheme (2008) or a second-order scheme that samples exactly the volatility component, and we show rigorously that we can achieve then any order of convergence. We give numerical illustrations on financial examples that validate the theoretical order of convergence. We also present promising numerical results for the multifactor/rough Heston model and hint at applications to other models, including the Bates model and the double Heston model.

翻译：本文基于Alfonsi与Bally（2021）提出的方法，构建了适用于Heston模型的任意阶弱近似方案。该方法通过组合在不同随机网格上计算的近似方案来提升收敛阶数。我们分别采用Ninomiya-Victoir方案（2008）与能精确采样波动率分量的二阶方案实施此方法，并严格证明了其可实现任意阶收敛。通过金融算例的数值模拟，我们验证了理论收敛阶的有效性。此外，本文展示了多因子/粗糙Heston模型的潜在数值结果，并探讨了该方法在Bates模型与双Heston模型等其他模型中的应用前景。