Statistical Inference For Hawkes Models Based On Financial Markets With Jumps

In recent years,the Hawkes process has gradually been applied to financial markets.Because it can fully depict the jump incentive effect of asset prices,it has attracted the attention of scholars.In the process of establishing the Hawkes model,it is the most important thing for scholars to choose an effective and accurate parameter estimation method.Bayesian estimation is one of the more popular estimation methods because it comprehensively considers the prior information of the parameters and the information of the sample data.Due to the comprehensive information considered,it has obvious advantages in the parameter estimation of the Hawkes model.In this thesis,the Hawkes model with exponential decay strength where the incentive term is constant is constructed for the jumping phenomenon of asset prices in the financial market.For this model,a more accurate model parameter estimation algorithm is established than the traditional maximum likelihood method,which is Bayesian inference based on Markov chain Monte Carlo(MCMC).The main research work is as follows:First,for the case of a single market,in order to study the time aggregation effect of its asset price jump,a unary Hawkes model with exponential decay strength where the incentive term is constant is constructed.For the three parameters in the model,the prior distribution of the parameters is first selected as the conjugate distribution.Then,combined with the likelihood function of the samples in the model,the conditional posterior distribution of each parameter is derived,and the Metropolis-within-Gibbs algorithm in the MCMC method is used to sam ple from the conditional posterior distribution of each parameter.For each parameter,the average value of all the sampled samples can be used to obtain the estimated value of the parameters in the model.Second,in the case of two markets,in order t o study the time and space aggregation effects of asset price jumps,based on the unary Hawkes model,a binary constant-incentive Hawkes model with exponential decay strength is constructed.At this time,there are ten parameters to be estimated in the model.As in the case of the univariate model,by combining the prior information of the parameters in the model and the likelihood function of the sampl e,the conditional posterior distribution of each parameter is derived,and then used a similar algorithm samples from th e conditional posterior distribution of the parameters to obtain the estimated values of the parameters.Third,using the thin algorithm to simulate the jumping path of the sample of the unary and binary Hawkes model,and compared with the maximum li kelihood method,it is found that the Bayesian method is better in the parameter estimatio n process of the model.Forth,this thesis selects the Shanghai and Shenzhen 300 stock index spot market and the Shanghai and Shenzhen 300 stock index futures market for empirical analysis.By establishing the unary and binary Hawkes models of the jump phenomenon of the two markets and using the bayesian method for parameter estimation,it can be found that both the jumps of asset prices in the futures market and the jumps of asset prices in the corresponding spot market of Shanghai and Shenzhen 300 stock index have obvious self-incentive effect,and there is asymmetric cross-incentive effect between the two markets,that is,the occurrence of the spot market price jump of Shanghai and Shenzhen 300 stock index will increase the probability of the occurrence of the price jump of Shanghai and Shenzhen 300 stock index futures market,but not vice versa.This study portrays the extreme risk transmission mechanism of China's sto ck index futures and spot,and has certain guiding signifi cance for the risk control of the regulatory authority.