Vasicek Model,Dynamic NS Model And Bond Pricing

The Treasury bond yield curve is the benchmark interest rate for financial market operations,and the Treasury bond yield curve is also a basic tool for bond pricing.A detailed study of the term structure of interest rates,finding and building a stable mathematical model,estimating its parameters and evaluating its performance,is very important for bond pricing.With the continuous advancement of interest rate marketization in my country,the guiding significance of government bond interest rates for bond pricing has become more significant,and the research on the term structure of government bond interest rates has also become crucial.Characterizing the behavior of short-term market interest rates through stochastic processes can play an important role in bond pricing,which is also very important for the development of the bond market.Based on the dynamic NS model and the Vasicek model,this paper uses my country's inter-bank market treasury bond data from January 2010 to December 2020 to conduct an empirical analysis and study the advantages and disadvantages of these two interest rate term structure models.Secondly,this paper divides the state transition matrix into four different forms in the state space form of the dynamic NS model,constructs four different dynamic NS models,and uses them for empirical research to discuss the partial zero constraint of the transition matrix.Then it discusses the relationship between macroeconomic indicators and models by taking the dynamic NS model of all-element arrays as an example.Finally,this paper uses the Vasicek model to calculate the theoretical price of treasury bonds,uses Kalman filter for parameter estimation,and deduces the pricing formula of treasury bonds under the interest rate model.The daily treasury bond transaction data is priced using the Vasicek model to give its theoretical price and compare it with the actual price.We found that for treasury bonds with short maturities,the Vasicek model has excellent pricing power,and the average error between the theoretical price and the actual price is within 1%,but as the remaining maturity increases,the theoretical bond theory given by the Vasicek model The error between the price and the market price shows an increasing trend.The conclusions of this paper are as follows: the four dynamic NS models can well fit and construct the term structure curve of the interbank government bond interest rate,and the fitting effect has little difference;the full-element dynamic NS model has a better fit than the other three models The fitting result of the upper triangular dynamic NS model is better than that of the diagonal dynamic NS model and the lower triangular dynamic NS model,but the difference is not very large.Array dynamic NS model,if we pursue the accuracy of the fitting results,we can choose the full-element matrix dynamic NS model,if we want to take both into account,we can choose the upper triangular array dynamic NS model;The initial value of the parameters of the Vasicek model is obtained by analyzing the repurchase rate of the national debt,and then the dynamic NS model of the diagonal matrix is used to estimate the daily yield data of the national debt during the sample period,and the parameter valuation of the three-factor Vasicek model is obtained through Kalman filtering.The inter-bank market treasury bonds can be priced;the error between the theoretical price priced by the three-factor Vasicek model and the actual market price tends to increase gradually with the increase of the remaining maturity;after the three-factor Vasicek model is revised,the Vasicek model's The pricing error has dropped significantly,and the model is more ideal for simulating the price of treasury bonds.