Lecture: Annalena Mickel, University Mannheim
Abstract: We study the L^1-approximation of the log-Heston SDE at discrete time points by equidistant explicit Euler-type methods. We establish the convergence order 1/2-epsilon for epsilon>0 arbitrarily small, if the Feller index of the underlying CIR process is larger than 1. For the L^1-approximation at the final time point this convergence order is optimal, since we also show that arbitrary methods which use an equidistant discretization of the driving Brownian motion can achieve at most order 1/2 in this case. Moreover, we discuss the case of a Feller index smaller than 1 and illustrate our findings by several numerical examples. Finally, we give an outlook on the possible generalization of our results.
|Veranstaltende||Lehrstuhl Prof. Dr. Thomas Prof. Müller-Gronbach,|
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