On arbitrarily slow convergence rates for strong numerical approximations of Cox–Ingersoll–Ross processes and squared Bessel processes

Mario Hefter () and Arnulf Jentzen ()
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Mario Hefter: Universität Kaiserslautern
Arnulf Jentzen: Eidgenössische Technische Hochschule Zürich

Finance and Stochastics, 2019, vol. 23, issue 1, No 4, 139-172

Abstract: Abstract Cox–Ingersoll–Ross (CIR) processes are extensively used in state-of-the-art models for the pricing of financial derivatives. The prices of financial derivatives are very often approximately computed by means of explicit or implicit Euler- or Milstein-type discretization methods based on equidistant evaluations of the driving noise processes. In this article, we study the strong convergence speeds of all such discretization methods. More specifically, the main result of this article reveals that each such discretization method achieves at most a strong convergence order of δ / 2 $\delta /2$ , where 0

Keywords: Cox–Ingersoll–Ross process; Squared Bessel process; Stochastic differential equation; Strong (pathwise) approximation; Lower error bound; Optimal approximation; 60H10; 65C30 (search for similar items in EconPapers)
JEL-codes: C22 C63 G17 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00780-018-0375-5

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