We study the $L^1$-approximation of the log-Heston SDE at the terminal time point by arbitrary methods that use an equidistant discretization of the driving Brownian motion. We show that such methods can achieve at most order $ \min \{ \nu, \tfrac{1}{2} \}$, where $\nu$ is the Feller index of the underlying CIR process. As a consequence Euler-type schemes are optimal for $\nu \geq 1$, since they have convergence order $\tfrac{1}{2}-\epsilon$ for $\epsilon >0$ arbitrarily small in this regime.
翻译：我们研究在终点点对 Heston SDE 的日志使用任意方法,对驱动布朗动议的驱动程序采用等距离分解法,以1美元为单位,在终点点对正对 Heston SDE 进行以1美元为单位的调整。我们表明,这种方法最多可以达到1美元(min)\\\ nu,\ frac{1\2} $(美元)\ nu$(美元)是基础 CIR 过程的Feller 指数。因此,Euler型计划对$\ nu\ geq 1美元来说是最佳的,因为在这个制度中,Eurer-sy-typroduc $\ tfrac{1\%2}-\ epsilon$(美元)为单位小于0.0美元(epslon)的任意价格。
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