带跳的随机利率模型的长时间行为分析及实证研究

Long-Term Behavior of Stochastic Interest Rate Models with Jumps and Memory

【目的】为了更好地反映周期性经济环境或未来货币预测对时间的依赖性。【方法】假设短期利率模型有一个随机回归水平,利用鞅定价方法及相关的数学工具展开讨论,综合考虑了随机利率模型的3个特征,分别是关于利率水平的延迟性、跳跃性和回归水平的时间依赖性。【结果】依据上海银行间同业拆借利率(Shanghai interbank offered rate,Shibor)数据,采用WLS回归分析方法对CIR随机利率模型进行实证研究,发现拟合曲线趋于水平。【结论】得到了长期投资回报几乎处处收敛到随机回归水平的结论。

[Purposes]In order to better reflect the dependence on time,which is caused by the cyclical economic environment or the prediction of the impact of future monetary.[Methods]Martingale pricing method and related mathematical tools are used to study,by assuming that the short-term interest rate model has a random reversion level,considering the three characteristics of stochastic interest rate model,namely,the delay,jump and time dependence of reversion level.[Findings]At the same time,based on the overnight Shibor data of Shanghai interbank offered rate,the WLS regression analysis method was used to conduct an empirical study on the CIR stochastic interest rate model.It is found that the fitted curve tends to be horizontal.[Conclusions]Revealing that longterm benefits almost certainly converge to a random reversion level.