Journal of Computational Finance

Sharp L¹-approximation of the log-Heston stochastic differential equation by Euler-type methods

Annalena Mickel and Andreas Neuenkirch

  • Strong approximation of CIR process and log-Heston model by Euler-type methods.
  • All Euler-type schemes from the literature are covered and polynomial convergence orders are obtained.
  • Convergence order 1/2, if the CIR process does not hit zero.

We study the L1-approximation of the log-Heston stochastic differential equation at equidistant time points by Euler-type methods. We establish the convergence order 1/2 – ∊ for ∊ > 0 arbitrarily small if the Feller index v of the underlying Cox– Ingersoll–Ross process satisfies v > 1. Thus, we recover the standard convergence order of the Euler scheme for stochastic differential equations with globally Lipschitz coefficients. Moreover, we discuss the v ≥ 1 case and illustrate our findings with several numerical examples.

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