Exponential integrability properties of euler discretization schemes for the Cox-Ingersoll-Ross process

Journal article

We study exponential integrability properties of the Cox-IngersollRoss (CIR) process and its Euler discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of stochastic differential equations arising in finance. We prove that both implicit and explicit Euler-Maruyama discretizations for the CIR process preserve the exponential integrability of the exact solution for a wide range of parameters, and find lower bounds on the explosion time.

Authors: Cozma, A; Reisinger, C

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Institute of Mathematical Sciences
• Journal: Discrete and Continuous Dynamical Systems - Series B
• Volume: 21
• Issue: 10
• Pages: 3359-3377
• Publication date: 2016-12-01
• Acceptance date: 2016-08-01
• DOI: 10.3934/dcdsb.2016101
• EISSN: 1553-524X
• ISSN: 1531-3492
• Keywords: stochastic volatility model; implicit Euler scheme; Cox-Ingersoll-Ross process; explicit Euler scheme; exponential integrability