【摘要】 研究表明利率序列具有长记忆性，故本文使用分数布朗运动代替经典CIR模型中的几何布朗运动，构建分数CIR模型，并通过欧拉离散对分数CIR过程进行路径模拟。由于分数布朗运动的非马尔可夫性和增量不独立，无法使用极大似然估计和马尔可夫链蒙特卡洛方法对分数CIR模型进行参数估计，故本文引入间接推断估计法，并通过蒙特卡洛模拟证明该方法的可行性。本文使用间接推断估计法对我国银行间同业拆放利率数据进行实证分析及样本外预测，将经典CIR模型、分数O-U过程、分数CIR模型的拟合轨道与真实轨道进行分析对比，得出分数CIR模型更适用于描述具有长记忆性的利率序列。本文重点研究一种用于分数CIR模型的参数估计方法，未来将继续探究其他参数估计方法并对比这些方法的有效性和稳健性。更多还原

【Abstract】 Research shows that the interest rate series has long memory, and this paper uses fractional Brownian motion to replace the geometric Brownian motion in the classical CIR model, constructs a fractional CIR model, and simulates the path of the fractional CIR process through Euler discretization.Because the non-Markov property and the increment of fractional Brownian motion is not independent, the maximum likelihood estimation and Markov chain Monte Carlo method cannot estimate the parameters of fractional CIR model, so indirect inference estimation is introduced. Monte Carlo simulation results show that this method can effectively estimate the parameters of fractional CIR model. This paper makes an empirical analysis with indirect inference estimation based on SHIBOR, makes out-of-sample predictions,compares the simulation orbit of the classical CIR model and the fractional O-U process and the fractional CIR model with the real orbit, and concludes that the fractional CIR model is more suitable for the interest rate series with long memory. This paper only focuses on a parameter estimation method for fractional CIR model; in the future, we will continue to explore other methods and compare the effectiveness and robustness of these methods.更多还原