基于非对称扩散跳跃过程的利率模型研究

A Research on Interest Rate Model Based on Asymmetric Diffusion Jump Process

在短期利率的扩散跳跃模型基础上,进一步考虑了模型扩散项方差自相关性、非对称性以及跳跃项的均值回复性等设定,以捕捉短期利率的均值回复、波动率集聚、非零偏态和超额峰度以及非连续性等特征。利用上海银行同业拆放市场(SHIBOR)日交易利率数据得出以下结论。首先,SHIBOR利率市场存在均值回复效应,由跳跃设定引起的混合正态分布能捕捉利率增量的尖峰特征。其次,利率增量方差遵循显著的非对称自相关过程,且正的冲击会产生更大的波动性,导致有偏分布。最后,跳跃是利率均值回复速率的重要组成部分,也是利率的水平值动态尤其是波动性动态的重要来源。

Based on the specification of diffusion iump in the short interest rate model, the paper furtherly takes the consideration of autocorrelation and asymmetry in variance of diffusion term, and mean reversion in jump term, aiming at capturing the feature of mean reversion, volatility cluster, nonzero skewness and extra kurtosis in short interest rate market. With the SHIBOR daily data, the paper gives three conclusions. Firstly, the model can reflect the mean reversion effect of interest rate market, while the weighted average of two normal variables under specification of jump term can successfully capture the leptokurtosis of interest rate change. Secondly, the variance of change in interest rate follows the significant asymmetric autocorrelation process, and the positive unexpected information will produce more volatility, which can produce nonzero skewness. Thirdly, jump plays a critical statistics role in SHIBOR market, which is the important source of mean reversion, and the dynamics of level and volatility of interest rate.