We propose here an approach in order to estimate parameters of the CIR model with jumps in the case where the distribution of jump amplitude is estimated non-parametrically. Since the knowledge of the exact distribution of the jump amplitude is a challenge, in this paper we choose not to fix this law in advance but to estimate it on the basis of the available observations. The method of estimation we propose here is based on the approximation of the closed form of transition density. Since the CIR does not have an explicit solution, it is approximated by the second order Milstein scheme in order to have a more accurate approximation. The method of estimation is then applied on real data, which are the Federal Funds rate and 3 Month T-Bill rate. These two sets of data are used to estimated parameters of the CIR model. We then compare our results to those obtained from Vasicek and Brennon–Swartz models with jumps. Results indicate that there is no clear winner of models competitions. Apparently depending on the nature and structural components of the data, there is a winner. The challenge here is that, there is a trade off between the sample size, the number of jumps and the efficiency of estimates. More data involves the likelihood to have more jumps and thereby less efficient are estimates.

我们在这里提出一种方法，以便在非参数地估计跳跃幅度的分布的情况下，估计具有跳跃的CIR模型的参数。由于了解跳跃幅度的确切分布是一个挑战，因此在本文中，我们选择不预先确定该定律，而是根据可用的观测值对其进行估计。我们在此提出的估算方法基于过渡密度的封闭形式的近似值。由于CIR没有明确的解决方案，因此可以通过二阶Milstein方案对其进行近似，以便获得更准确的近似值。然后将估算方法应用于真实数据，即联邦基金利率和3个月国库券利率。这两组数据用于估计CIR模型的参数。然后，我们将我们的结果与从带有跳跃的Vasicek和Brennon-Swartz模型获得的结果进行比较。结果表明没有明确的模型竞赛获胜者。显然，取决于数据的性质和结构成分，会有一个赢家。这里的挑战在于，样本量，跳跃次数和估计效率之间需要权衡。数据越多，跳跃的可能性就越大，从而估计的效率就越低。