一个动态瞬时远期利率模型研究—基于HJM 模型

摘要
在现代金融分析中，远期利率占据着越来越重要的地位，在成熟市场中几所有利率衍生品的定价都依赖于远期利率，但在利率期限结构研究中，大部分率模型（如均衡模型）均不能很好地拟合观察到的远期利率数据，模型估计出远期利率理论值与市场上观察到的实际值相差很大。

因此，本文主要研究瞬时期利率模型，建立的模型满足HJM 无套利条件。

首先，本文阐述了中国正进行利率市场化进程这一研究背景，研究利率期
结构所具有的重要理论意义和现实意义，以及本文研究瞬时远期利率模型的义。

接着，本文比较系统地回顾了国内外关于利率期限结构静态和动态研究的展过程，各种模型的优缺点，以及模型参数估计方法。

然后，本文对瞬时远期率进行建模，把瞬时远期利率分为三个部分：非条件下的远期利率、与特定期相关的偏差成分、与特定日期相关的偏差成分。

本文把这三个部分都参数化为个指数函数之和，最终得到的瞬时远期利率模型是一组参数少、状态变量个数活的模型，且这些模型均满足HJM 无套利条件。

在实证研究方面，本文先用静NSS 模型从国债价格数据中估计出瞬时远期利率值，再根据对数似然函数值AIC 准则从本文建立的七个候选瞬时远期利率模型中选取一个对这些瞬时远利率数据拟合得最好的模型。

接着本文执行Kalman Filter 方法估计出该最优型的参数，并分析该模型的实证结果。

最后本文对该模型进行样本外预测，计了两个指标来评价预测效果——均方差根和相对均方差根，并得出该模型在预方面表现很好的结论。

关键词：远期利率；无套利条件；卡尔曼滤波
Abstract
The analysis of forward rates is a benchmark in the modern financial analysis. Most of the interest rates derivative pricing largely depends on the forward rates. However, most interest rate models (such as equilibrium models) cannot fit the real forward rate data well. Actually the predicted forward rate values by those models are far different from the real data. Therefore, this paper concentrates on the modeling of instantaneous forward rates, which satisfies the HJM No-Arbitrage condition.
This paper first expatiates on the background of this research: China is on the market-oriented process of the interest rate. Then this paper discusses the theories and application significance of the study on the term structure of interest rate, and the significance of the study on the model of instantaneous forward rate in this paper. Furthermore, this paper reviews systematically the static and dynamic studies on term structure of interest rate, the advantage and defect of all kinds of the models, and the corresponding parameter estimation methods of the models. Moreover, this paper models the instantaneous forward rate, which is developed as the sum of (i) an unconditional or steady-state component, (ii) a maturity-specific deviations component and (iii) a date-specific deviations component. The three components are all parametrically constructed as a sum of exponential functions, and the resulting forward rate models are a class of low-parameter, flexible-state variables dynamic models, and all satisfy the HJM no-arbitrage condition. In the empirical part, this paper first estimates the instantaneous forward rate of the government bonds price using the NSS models. Then this paper selects a model from the seven candidate forward rate models that fits these instantaneous forward rate data best by log-likelihood and AIC. Furthermore, this paper estimates the parameters of the selected instantaneous forward rate model by the Kalman Filter method, and analyzes the empirical output of this model. Finally, this
paper forecasts the out-of-sample bonds price using this model, then calculates two indicators, RMSE and relative RMSE (RRMSE), to evaluate the forecasting effect, and concludes that this model performs well in the aspect of forecasting.
Key Words: Forward Rate; No-Arbitrage Condition; Kalman Filter。