Heavy tail and light tail of Cox-Ingersoll-Ross processes with regime-switching

This study aims to investigate the tail behavior of Cox-Ingersoll-Ross (CIR) processes with regime switching. An essential difference shown in this study between CIR processes with and without regime switching is that the stationary distribution of those with regime switching may be heavy-tailed. We...

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Bibliographic Details
Published in:Science China. Mathematics 2020-06, Vol.63 (6), p.1169-1180
Main Authors: Hou, Tongtong, Shao, Jinghai
Format: Article
Language:English
Subjects:
Applications of Mathematics
Interest rates
Markov analysis
Mathematics
Mathematics and Statistics
Switching
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Summary:This study aims to investigate the tail behavior of Cox-Ingersoll-Ross (CIR) processes with regime switching. An essential difference shown in this study between CIR processes with and without regime switching is that the stationary distribution of those with regime switching may be heavy-tailed. We first provide sharp criteria to justify the existence of a stationary distribution for the CIR process with regime switching, which is applied to study the long-term returns of interest rates. Then, we provide a criterion to identify whether this distribution is heavy-tailed. Our results provide theoretical evidence of the existence of regime switching for interest-rate models based on empirical evidence of a heavy-tailed distribution.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-017-9392-5