The Comparative Study Of Affine Interest Rates Term Structure Models

The term structure of interest rates is widely used in the field of finance and economy, it can provide certain reference for investors in asset pricing, arbitrage, hedging and risk management. In addition, the term structure of interest rates has certain conduction ability for monetary policy and inextricably linked with macro economy. Afifine model is one of the term structure of interest rates model, it is more simple than other models and easy in parameter estimation, above all, it has reasonable economic interpretation. So, we make a comparative study of multiclass affine models for providing empirical evidence for model selection.Firstly, we classify for affine model by volatility and risk price form. Based on the model characteristics and the result of factor analysis in interbank interest rates data, eventually, we choose two factors, three factor CIR model, Vasicek model and Extended Gaussian affine model. We want to compare to these models from fitting effect of yield curve' cross section information and prediction effect of interest rate changes.Secondly, we choose the interest rate term structure data of Chinese inter-bank bond and US Treasury bond to make empirical study. We find the conclusions as follows. Overall, the three factor model is slightly better than the two factor model, the Extended Gaussian model is better than the CIR model, Vasieck model. From the shape fitting effect, the extended essential affine is better than the fully affine in the form of risk price; When the volatility of short-term interest rate is greater than the long-term interest rate, the Gaussian process is better than the root mean square process in the form of volatility. From forecast effect of interest rate change, when the risk price from is extended essential, the model can improve to prediction effect of interest rate changes under maintaining yield curve fitting effect.Thirdly, we build the Macro-finance model of interest rate term structure on the basis of the Extended Gaussian affine model with some macroeconomic policy variables added. Compared with the traditional Extended Gauss affine model, the Macro-finance model has better fitting effect on the cross section information of yield curve and forecasting ability in interest rate changes; the forecasting effect of the model on long term interest rate changes is better than that of the short-term. In addition, we investigate the relationship between the macro economy and the term structure of interest rates by impulse response and variance decomposition. We find the conclusions as follows. There is a strong relationship between inflation with the level factor and the slope factor. It provides a very good interpretation for that the macro finance model have better prediction effect on the long-term interest rates change. In addition, so the factor level and slope factor of inter-bank treasury bond interest rate term structure can be used to predict future inflation, and the term structure of interest rates have conduction ability for monetary policy.Finally, by comparing Chinese and American empirical results, we found that in the efficient United States bond market, all of models can to some extent reflect the predictability of future interest rate changes, but in the bond market in China, the performance is unsatisfactory. As can be seen, the efficiency of China's bond market needs to be improved, the interaction between term structure of interest rate and macro economy needs to be strengthened.