Research On Pricing Of Shanghai 50ETF Option Based On Levy-GARCH Model

China's first exchange option of Shanghai 50 ETF has been officially traded in the Shanghai stock exchange on February 9 in 2015,which opened the beginning of China's options era.However,the core of the option is pricing,and the discovery of reasonable price is the basis of all trades,such as hedging and speculative arbitrage.At the same time,as a type of financial derivatives,option's value mainly depends on the value of the underlying assets changes.Therefore,the research on the Shanghai 50 ETF option pricing and the characteristics of its underlying assets are the focus of this article.Many foreign literature studies have shown that there are random jump behaviors,conditional heteroskedasticity and leverage effect in the capital market.Although research on the Chinese capital market also found that there are significant jump behaviors and heteroskedastic characteristics,but leverage effect is not a universal feature.Among them,the underlying asset of China's only listed option does not exist leverage effect.Leverage effect refers to negative shocks that cause greater volatility.Therefore,in order to jointly characterize the random jump behavior and dynamic volatility characteristics of the capital market and study the leverage effect of the Shanghai 50 ETF market,this paper uses the Levy-GARCH model to empirically study the Shanghai 50 ETF market and its option.This paper is main divided into three portions.First,respectively builds three Levy process such as continuous diffusion process,limited jumping process,infinite jumping process,combined with dynamic volatility model such as GARCH model,NGARCH model,using maximum likelihood estimation and MCMC method to study the fitting degree of the logarithmic yield distribution of Shanghai 50 ETF.Second,through several kinds of model's characteristic functions,calculates the model under the risk neutral measure,and obtains the parameter relationship after the measurement transformation.Third,simulates Shanghai 50 ETF price road under several kinds of models using Monte Carlo process,obtains the theoretical option price,to study the performance of different models in the pricing of Shanghai 50 ETF options.The empirical research shows that,first,in terms of model,the Levy process is significantly better than normal distribution in the fitting degree of the log-returns yield of the Shanghai 50 ETF,and the GARCH model driven by infinite activity Levy process has higher fitting degree.Second,for the method,the numerical maximum likelihood estimation is consistent with the parameter estimation result of the MCMC method,which shows the robustness of the parameter estimation.In addition,this paper proposes to study the Shanghai 50 ETF market using the high-efficiency and highprecision numerical maximum likelihood estimation method for the Levy-GARCH model within a large sample interval.Third,for option pricing,the dynamic volatility model driven by the Variance Gamma process has the highest pricing accuracy by comparing the root mean square error and average relative error of different models,which is also the same as the conclusion of the model in terms of goodness of fit.Therefore,there is enough evidence to show that the Variance Gamma model can fully characterize the characteristics of the Shanghai 50 ETF market.Four,leverage effect does not exist in the Shanghai 50 ETF market which is significantly different from the foreign capital market.For exploring reasons,the analysis will be presented in following aspects: industry characteristics,features of constituent stocks and market mechanism.Our country strongly supports the development of the derivatives market and is constantly striving towards internationalization.In the short term,the correct understanding of option price will help investors make the right investment strategy.In the long run,it is conducive to the stability of the capital market to learn the reasonable option pricing method.Therefore,this article has a significant practical significance to the study of the pricing of the Shanghai 50 ETF options.