Asymmetric Interval Estimation Of Short-term Interest Rate Jump Diffusion Model Based On Empirical Likelihood

With the continuous improvement of China's financial marketization,China is currently gradually transforming its monetary policy operating mechanism,that is,transforming its monetary policy operating mechanism based on bank credit into a market-based monetary policy operating mechanism.In order to improve the existing market-oriented financial market operation mechanism,in addition to ensuring the stable operation of the financial market,in addition to increasing the sensitivity of micro-subjects in the market to price setting,the effectiveness of monetary policy should be ensured to cope with the current complex international and domestic The impact of the situation on financial markets.The marketization of interest rates has achieved phased results under the influence of international monetary policy,which has reduced friction in the transmission of monetary policy and improved the financial market environment.At present,the interbank rate,the interbank repo rate and the SHIBOR rate can all be used to characterize the benchmark interest rate.Therefore,accurately estimating the fluctuation of the benchmark interest rate can further provide quantitative guidance for China's price-oriented monetary policy.In order to more accurately describe the changes in interest rates,in recent years people usually use the diffusion model with jumps to characterize the spot volatility of interest rates.Because of the existence of jump terms in the model,it is more statistically general than the previous diffusion model Model.In the jump diffusion model,the coefficient of the spread of the interest rate is the volatility of the interest rate.In the jump diffusion model,its parameter estimation usually requires a priori assumption of data characteristics such as parameter distribution,and non-parametric estimation methods do not impose related restrictions.The method based on non-parametric kernel estimation requires relatively little prior information generated by the underlying data,and the obtained estimation results are usually robust.In the existing literature,when estimating the volatility,the continuous situation and the jump situation are usually combined to estimate.However,the probability of jumps is usually small and the frequency is low.Therefore,estimating the jump terms together will cause a certain deviation.The purpose of this study is to use the empirical likelihood estimation data-driven characteristics based on the jump diffusion model,use non-parametric forms to estimate the drift coefficient and volatility terms in the interest rate model,and use the Garch model to jump in the jump diffusion The term is eliminated,and an asymmetric confidence interval is constructed according to the characteristics of the data,which reflects the direction of volatility change and improves the coverage of the volatility term estimation result of the diffusion model.Study the fluctuation of SHIBOR interest rate and provide support for the further development of interest rate liberalization in China.In the case of considering jumps,this paper uses empirical likelihood estimation for the single-factor short-term interest rate under continuous time,and through mathematical derivation,proves the rationality of the threshold estimator and estimates the confidence interval of the volatility.The advantages of empirical likelihood estimation over asymptotic normal estimation are illustrated from two aspects of mathematical proof and stochastic simulation.The main advantage is that the confidence interval constructed by the empirical likelihood method has higher coverage.It can reflect the actual situation of the real data more accurately from a data-driven perspective,and can further obtain an asymmetric confidence interval,which can reflect fluctuations to a certain extent.Rate change direction.The simulation results are as follows: 1.For the same model Xt,when the data amount n is the same and the bandwidth h is different,the confidence interval coverage estimated by the empirical likelihood is stable and fluctuating around 90%,but it is asymptotic.The confidence interval of the normal estimation fluctuates greatly with the change of bandwidth,so it shows that the empirical likelihood coverage is not sensitive to the change of bandwidth.2.When keeping the same amount of data n and the same bandwidth h,when the observation points x = 0.04 and 0.14,the effect of asymptotic normal coverage will be relatively poor,especially when the bandwidth is large.This is because the frequency of the simulated jump diffusion process passing through the 0.04 and 0.14 spatial points is relatively low,so the sample size is insufficient when estimating these two points,which can be seen from L in the local estimation.Therefore,relative to the estimated point of 0.08 with a large locality,under the same bandwidth,x = 0.04 and 0.14 have longer confidence interval lengths.3.For the same data amount n,estimated point,and bandwidth,the second set of parameters has a shorter confidence interval length because ? is smaller.4.For both models,the result coverage of the empirical likelihood estimation is higher than the asymptotically normal estimated coverage,which illustrates the effectiveness of the construction estimation method in this paper.This article uses Shibor interest rate and Libor to compare from two empirical perspectives.Based on the empirical results,the following suggestions are proposed: increase the participation of non-bank institutions in quotation;add pricing products based on Shibor interest rate;improve information disclosure and establish a credit evaluation mechanism.