Modeling And Estimating Short-term Interest Rate

As one of the most important and the most basic economic variables in the financial markets, short-term risk-free rate reflects the pure time-value of money and has an important guiding role on intertemporal configuration of asset. It is also an important basis for all assets pricing, which can derive risk benefit. It is the pricing benchmark for all risk assets, such as stocks, bonds, options and so all. Short-term risk-free rate plays a pivotal role for pricing other financial products and managing the interest rate risk. It also reflects the supply and demand relationship of short-term money and it is an important weathervane of the country’s economic situation.With the quickening step of interest rates liberalization, the supply and demand of fund in financial market, which is restricted and influenced by many factors, becomes a major influence factor for changes of interest rates. Therefore it will lead to frequent changes in interest rates inevitably. Interest rate fluctuations will have a greater impact on the macroeconomic, stock market and of financial institutions. Thus, how to predict fluctuations of interest rate and prevent interest rate risk becomes a significant research topic for the financial institutions in the context of interest rate liberalization. How to model interest rates and how to portray the dynamic characteristics of term structure of interest rates effectively, thus we can forecast future changes of interest rates scientifically, will be worth of study and has significant theoretical significance and application value.A mass of empirical studies at home and abroad have found that short-term changes in interest rates have spikes, thick tail, a skewness of distribution, and its time series volatility clusters. Thus, the general time-series models to fit the volatility of financial data become less suitable. Some domestic and international literature commonly used parametric and semi-parametric methods to characterize the short-term interest rate volatility, but these two methods exist misspecification and the "curse of dimensionality" defect, their performance in explaining the practical problems is not strong. To avoid these problems, semi-parametric approach, as an appropriate middle approach, cause great attention. This method is a integrate of parametric and non-parametric approach, it can not only overcome the misspecification defect of parametric method, but also can solve explained the lack of capacity and the "curse of dimensionality" dilemma non-parametric method. So semiparametric method have great value for academics and investors. Currently, the semi-parametric methods which are increasingly employed in the financial sector, is a powerful tool to measure the volatility of financial markets. In this paper, we use this semi-parametric approach to model and estimate the short-term interest rate volatility of China.Researching volatility of the financial assets returns is central area of the contemporary financial economics and econometrics study. As a measure of market risk, the identification of volatility will directly affect the asset pricing, resource allocation and risk management modeling. On the one hand, volatility is directly relevant to market uncertainty and risk. The increase of Volatility implies risk increasing. High-risk will have larger influence on the business operations. And the equalization of returns---risk is the core of capital allocation and asset pricing. On the other hand, volatility is closely related to other indicators which reflect the quality and efficiency of the stock market. These indicators, which include liquidity, transparency, transaction costs, market efficiency, information flow characteristics, etc., is one of the most concise and effective indicators to reflect the stock market price behavior, quality and efficiency synthetically. In addition, volatility plays an underestimated role for the decision-making of enterprise financial leverage, operating leverage and investment leverage, the personal consumption and investment behavior, as well as the economic cycle and related macroeconomic variables. Just because of this, volatility becomes a constant theme in the financial market.In this paper, we select daily data of the Shanghai Interbank Offered Rate for one week as the research sample to make a research on the short-term interest rate of China. By making statistical analysis on SHIIBOR1W daily data through January4,2007to March201320period, we found that the SHIBOR1W time series of interest rate sequences have non-normality and conditional heteroscedasticity characteristics. Compared with the normal distribution, SHIIBOR1W presents leptokurtosis and non-normal distribution pattern. Short-term interest rate volatility has a cluster, i.e. large fluctuations will be followed by large fluctuations, while the relatively small fluctuations also appeared behind the small fluctuations, which is consistent with the study findings on volatility of the mature financial market. Then in order to compare the several models further, we use parametric methods and semi-parametric methods respectively for modeling and estimating SHIBOR1W interest rate sequence, consider the sequence of residuals follows a normal distribution or student t distribution or GED distribution situation. Sequentially, we can obtain the best model that simulates SHIBORIW rate fluctuations. The empirical findings illustrate that the semiparametric model is significantly better than the parametric model on predictive ability of interest rates volatility. The last chapter is conclusion and prospect, which provides a reference for the further deepen study of the risk characteristics of the money market.On the basis of the empirical results, we obtain the following summing-ups:1) According to the maximum likelihood value, the EGARCH model with the hypothesis of Student’s t-distribution is superior to other parameter models, while the GARCH model with the normal distribution is the worst. This is because the GARCH model fails to capture the non-symmetry and level-dependent in the short-term interest rate volatility process.2) By analyzing the predictive power of each model when its innovation follows the normal distribution, Student’s t distribution or GED distribution respectively, we get the conclusion that supports the use of Student’s t-distribution, and normal distribution and GED distribution is not suitable.3) From the goodness of fit of parametric and semi-parametric method term, EGARCH model runs optimal effect. However, compared to the EGARCH model, semi-parametric methods have greatly improved forecasting ability in terms of volatility. The volatility fitting performance of the semiparametric procedure, unlike the parametric GARCH models, is also robust to different hypothesis in the innovation distribution.