Sharp L^1-Approximation of the log-Heston SDE by Euler-type methods
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We study the L^1-approximation of the log-Heston SDE at equidistant time points by Euler-type methods. We establish the convergence order 1/2-ϵ for ϵ >0 arbitrarily small, if the Feller index ν of the underlying CIR process satisfies ν > 1. Thus, we recover the standard convergence order of the Euler scheme for SDEs with globally Lipschitz coefficients. Moreover, we discuss the case ν≤ 1 and illustrate our findings by several numerical examples.
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