The order barrier for the L^1-approximation of the log-Heston SDE at a single point

12/14/2022

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by   Annalena Mickel, et al.

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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{ν, 12}, where ν is the Feller index of the underlying CIR process. As a consequence Euler-type schemes are optimal for ν≥ 1, since they have convergence order 12-ϵ for ϵ >0 arbitrarily small in this regime.