A Dynamic Model For The Instantaneous Forward Rate

The analysis of forward rates is a benchmark in the modem 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.