Shibor Dynamic Research Based On Nonparametric Estimation Of Variable Window Width Of Jump Diffusion Model

The interbank interbank borrowing market interest rate,as the first open interest rate after China officially entered the process of interest rate liberalization,has an important impact on economic activities.In order to promote the marketization of interest rates,the People's Bank of China launched the Shanghai Interbank Offered Rate,Shibor,as the benchmark interest rate for China's money market on January 4,2007.Due to the impact of the economic environment,its volatility characteristics have important research value.At present,the academic research on Shibor mainly focuses on its feasibility and stability.This paper will focus on the volatility of Shibor and provide ideas and methods for better understanding the characteristics of China's interest rate market.Through domestic and foreign research,it is found that important macroeconomic events will cause fluctuations in the interest rate market.This paper finds that the sudden large fluctuations are closely related to the important economic events occurring in the corresponding time through the observation of the Shibor overnight data.The jump feature is important for controlling interest rate risk.The jump diffusion model is one of the effective models for characterizing short-term interest rates.In this paper,the variable window width non-parametric estimation method and the constant kernel estimation(NW estimation)method are used to estimate the coefficients of the model to verify that the variable window width is introduced to improve the estimation accuracy.Firstly,through the Monte Carlo simulation,the variable window width estimation and NW estimation are carried out for the drift coefficient and the diffusion coefficient of the two jump diffusion models respectively.The comparison of the error indicators shows that the variable window width estimation is closer to the true value and the related settings are changed.The fixed parameters and the method of setting the fixed orbit are carried out in multiple simulation experiments to prove the robustness of the variable window width estimation,which provides a theoretical basis for accurately measuring the fluctuation behavior of interest rates.In the empirical analysis,this paper takes the 2007-2017 Shibor interest rate as the research object,and identifies the time linkage between its jumping characteristics and macroeconomic events.Through the stationarity analysis,Shibor's overnight data(O/N)is divided into test set and training set.The variable window width estimation method and NW estimationmethod are used to estimate the drift coefficient and diffusion coefficient.The comparison error index indicates that the variable window width estimation is applicable.In the description of the Shibor interest rate scenario,especially for data such as the Shibor interest rate jump phenomenon,the variable window width estimation value is more accurate.Therefore,this paper starts from the practical problem,in order to better study and fit the Shibor interest rate data with jumping behavior,replace the generalized interest rate model with the jump diffusion model to simulate the data,compare the advantages of the parameter estimation and the non-parametric estimation,and then introduce the change.In the idea of window width,it is proposed to use the variable window width non-parametric estimation method to estimate the model.The estimation method makes full use of the data information and greatly improves the estimation accuracy.After Monte Carlo's multi-dimensional simulation,the optimization and robustness of the variable window width estimation compared with the NW estimation are verified.It is also applied to the study of the volatility of Shibor data.It shows that the variable window width non-parametric estimation method can capture data information more accurately,and gives high-precision estimation,which also shows the practical economic application value of the method.