Exponential integrability properties of euler discretization schemes for the Cox-Ingersoll-Ross process
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 f...
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| Format: | Journal article |
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American Institute of Mathematical Sciences
2016
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| Summary: | 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. |
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