Jumping Analysis Of Shanghai,Hang Seng And Dow Jones Index Based On Jump Diffusion Model

With the rapid development of global economy and finance,people's investment and financial awareness gradually increased,then more and more funds began to flow into the financial industry.For China's stock market,national stock turnover quadrupled in just five years,which illustrate the stock market investment heat is unprecedented.The stock index can be used to quantify the volatility of the stock price,whose role is the economic barometer,or market indicator.The jump means the big change of the stock index.The big jump will lead to the uncertainty and instability of the economic and financial market.Therefore,there is great theoretical and practical significance to study the jumping of the stock market.At present,there are many models on volatility of stock index.But these models cannot explain big change that mean the jump of the index for the sudden event information.We choose the jump-diffusion model to calculate jump strength of the index based on what Merton proposed in 1976.Firstly,we use Bayesian inference to get the conjugate prior distribution and the posterior distribution of the parameters.Then,Markov Chain Monte Carlo(MCMC)method is used to estimate the parameters.The estimation model is obtained and finally the jump strength of the index model can be analyzed.For the empirical analysis,this paper uses pure diffusion process and jump diffusion process as model basis,and uses the data from the beginning of 2001 to the end of 2014 for the shanghai,hangseng,and Dow Jones index daily closing index.Therefore,we can easily construct the six models and estimate the parameters by MCMC method.Then we can make a comparison.Finally,this paper use the estimated model to predict the shanghai index from the beginning of 2015 to March 2017,respectively,to analyze the degree of fitting.By analysing above process,we can get the conclusion that the Shanghai and Hangseng index have a more obvious jump than the Dow Jones',and jump-diffusion model has a higher degree of model fit.