Levy过程驱动下的反射Cox-Ingersoll-Ross利率模型的平稳性

On the Stationary Property of a Reflected Cox-Ingersoll-Ross Interest Rate Model Driven by a Levy Process

  • 摘要: 布朗运动与正态分布已被广泛应用在Cox-Ingersoll-Ross利率框架的瞬时动态利率模型中, 然而, 实证研究表明, 利率的回报率分布比正常分布有一个更高的峰值和两个更胖的尾部. 同时, 当罕见的灾难性的冲击发生或在经济和金融的体制发生转变, 货币市场可能会出现跳. 在本文中, 我们将考虑一类带噪声的反射Cox-Ingersoll-Ross利率模型. 此外, 我们得出了这种带跳的反射扩散过程平稳分布的拉普拉斯变换.

     

    Abstract: Brownian motion and normal distribution have been widely used in Cox-Ingersoll-Ross interest rate framework to model the instantaneous interest rate dynamics. However, empirical studies have also shown that the return distribution of interest rate has a higher peak and two fatter tails than those of the normal distribution. Meanwhile, when the rare catastrophic shocks occur or the regime shifts in the economy and finance, the money market may have jumps. In this paper, we will consider a class of reflected Cox-Ingersoll-Ross interest rate models with noise. Furthermore, we shall continue to supply the Laplace transform of the stationary distribution about this reflected diffusion process with jumps.

     

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