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Modern Stochastics: Theory and Applications


Functional limit theorems for additive and multiplicative schemes in the Cox–Ingersoll–Ross model
Volume 3, Issue 1 (2016), pp. 1–17
Pub. online: 3 March 2016      Type: Research Article      Open accessOpen Access
Received
15 December 2015
Revised
22 February 2016
Accepted
25 February 2016
Published
3 March 2016

Abstract

In this paper, we consider the Cox–Ingersoll–Ross (CIR) process in the regime where the process does not hit zero. We construct additive and multiplicative discrete approximation schemes for the price of asset that is modeled by the CIR process and geometric CIR process. In order to construct these schemes, we take the Euler approximations of the CIR process itself but replace the increments of the Wiener process with iid bounded vanishing symmetric random variables. We introduce a “truncated” CIR process and apply it to prove the weak convergence of asset prices. We establish the fact that this “truncated” process does not hit zero under the same condition considered for the original nontruncated process.

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© 2016 The Author(s). Published by VTeX
Open access article under the CC BY license.

Keywords
Cox–Ingersoll–Ross process discrete approximation scheme functional limit theorems

MSC2010
60F99 60G07 91B25

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