In this paper, we study the excursions of Bessel and Cox–Ingersoll–Ross (CIR) processes with dimensions . We obtain densities for the last passage times and meanders of the processes. Using these results, we prove a variation of the Azéma martingale for the Bessel and CIR processes based on excursion theory. Furthermore, we study their Parisian excursions, and generalize previous results on the Parisian stopping time of Brownian motion to that of the Bessel and CIR processes. We obtain explicit formulas and asymptotic results for the densities of the Parisian stopping times, and develop exact simulation algorithms to sample the Parisian stopping times of Bessel and CIR processes. We introduce a new type of bond, the zero‐coupon Parisian bond. The buyer of such a bond is betting against zero interest rates, while the seller is effectively hedging against a period where interest rates fluctuate around 0. Using our results, we propose two methods for pricing these bonds and provide numerical examples.

中文翻译：

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贝塞尔（Bessel）和CIR流程的Azémamartingales以及巴黎零息票债券的定价

在本文中，我们研究了Bessel和Cox–Ingersoll–Ross（CIR）过程的尺寸偏差 。我们获得了最后通过时间和过程曲折的密度。使用这些结果，我们证明了基于偏移理论的the贝和CIR工艺的Azémamartingale的变体。此外，我们研究了他们的巴黎旅行，并概括了先前关于布朗运动的巴黎人停留时间到贝塞尔和CIR过程的停留时间的结果。我们获得了巴黎停止时间的密度的明确公式和渐近结果，并开发了精确的仿真算法来采样贝塞尔和CIR过程的巴黎停止时间。我们引入了一种新型的债券，即零息巴黎债券。此类债券的买方押注零利率，而卖方则有效规避利率在0左右波动的时期。使用我们的结果，