Nonparametric Jump Test Method And Its Jump Dynamic Analysis Based On Jump Diffusion Model

Economists use jumps to describe the phenomenon of sharp rises and falls in asset prices in financial markets.Based on the jump diffusion model,this paper studies the quadratic variation of the logarithmic asset price and gives its consistent estimator,that is,the realized volatility and the realized range.When the jump occurs,it is decomposed into integral variance according to the martingale of the asset price.In order to separate the jump variation from the quadratic variation,to study the consistent estimation of the integral variance,in order to solve the problem of the error in the integrated variance estimation of the quadratic variation,this paper proposes the modified threshold to achieve quadratic variation and the modified to achieve quadratic range.The main content of this paper is the detection of jumps.According to the existing BN-S jump test method,it can only detect whether there are insufficient jumps on a certain day.Based on the LM jump test idea,it is known that the return of standardized assets obeys the standard normal distribution asymptotically,and the theorem that the second-order moment process converges in probability is proposed.The theorem shows that substituting the pointin-time fluctuation obtained from the uniform estimation of the integral variance into the standardized asset return does not change its distribution,thus constructing two jump test statistics J?CTBPV and J?CRBV.This paper verifies the feasibility and effectiveness of the proposed method through Monte Carlo simulation analysis,and finally selects the 5-minute CSI 300 index future for empirical analysis.The conclusions are as follows:Firstly,Monte Carlo simulation studies show that the number of jumps detected by the BN-S test method is more than that of real jumps,while the number of jumps detected by J?CRBV,which is also used to detect day jumps,is less,but more robust strong;while the detection accuracy of the intraday jump detection methods LM and J?CTBPV is relatively high,and the conclusion shows that with the increase of sampling frequency,the detection accuracy is improved to varying degrees.Secondly,in the empirical analysis,the CSI 300 index is selected as the research object and preprocessed.The detection results of the four jump test methods are similar to simulation.BN-S has the largest number of jumps,J?CRBV is the least,and LM and J?CTBPV are in the middle.The study found that there are jumps in trading days,mostly on Monday,Thursday and Friday.The jumps during the stock market crash are more severe than those during the non-stock market crash,that is,the jump is larger,and the jumps have the characteristics of aggregation,continuity,and lag,which fully reflect the effect of assets in the financial market.