一类均值为跳跃-均值回复过程的利率模型  

Interest rate model with jump-mean reverting stochastic mean

作　　者：范龙振[1] 程南雁[1] 

机构地区：[1]复旦大学管理学院,上海200433

出　　处：《系统工程学报》2011年第3期298-305,共8页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(70971025)

摘　　要：中国的基准利率为1年期储蓄存款利率,其变化规律和对市场利率的影响不同于西方市场的基准利率,需要新的利率模型来反映基准利率的影响.本文用泊松过程描述1年期储蓄存款利率调整的发生次数,用扩散过程描述该利率调整大小及其时间序列相关性,并假定1年期储蓄存款利率决定了1年期市场利率的均值水平.在仿射模型的框架下,利用随机贴现因子定价模型,建立包含基准利率的连续时间仿射类利率模型,并利用MCMC(马尔科夫链蒙特卡洛)方法对之进行实证分析.实证分析说明本文给出的利率模型较好地拟合了市场利率期限结构的变化,并揭示了把1年期储蓄存款利率作为状态变量可以显著提高模型对市场利率期限结构数据的拟合精度.The benchmark interest rate in China is one-year deposit interest rate,and its change and effect on market rates are different to that in the developed markets.New interest rate model should be constructed to reflect effect of the benchmark rate in China.This paper uses a Poisson process to describe the change of the one-year deposit rate,and uses a diffusion process to describe its change size and reflect its serial correlation. It is assumed that mean of one-year market rate is determined with the one-year deposit rate.Under the framework of affine model,making use of stochastic discount factor asset pricing model,a continuous-time affine interest rate model including benchmark rate as a factor is established.The model is empirically tested with MCMC（Markov chain Monte Carlo）,and the results indicate that using one-year deposit rate as a factor improves the fit of model to data significantly,and the model matches the market yield curve very well.

关 键 词：基准利率 市场利率 泊松过程 仿射模型 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]