Quasi-Monte Carlo Simulation And Analysis Of GARCH Option Pricing Models

With the vigorous development of my country's financial market,options have long developed into indispensable commercial trading products in mature financial markets,so it is very meaningful to carry out research on option pricing issues.Choosing reasonable and accurate pricing methods can not only maintain the order of the option trading market,but also assist investors in making better options investment decisions.In practical applications,many scholars are accustomed to using Monte Carlo method for numerical simulation to calculate the numerical solution of options.However,the pseudo-random number sequence generated by this method is not uniform,which will lead to deviations in the calculation results,and the calculation amount is very large,and the convergence speed is very slow.It often requires a lot of experiments to get an accurate estimate.Therefore,many scholars have begun to try to use the quasi-Monte Carlo method to study the issue of option pricing.The quasi-Monte Carlo method generates a quasi-random number sequence,which can reduce the number of trials and improve the accuracy and calculation speed of estimation.The sample data selected in this article is the daily closing price data of the SSE 50ETF,and the selected sample data time interval is from February 9,2015 to May 25,2016.First,use Matlab software to preprocess the selected data to establish a GARCH option pricing model,including GARCH,EGARCH,and TGARCH three models.The volatility from May 26 to July 27,2016 is predicted through numerical simulation,and the volatility data predicted by the three models are brought into the BS equation,and the Monte Carlo method and the quasi-Monte Carlo method are used to perform multiple calculations.In this simulation,the numerical solution of the option is obtained after calculation,and then the option price calculated by the two methods is compared with the real value,and a conclusion is drawn.Through numerical experiments,it is confirmed that the quasi-Monte Carlo method is more accurate in numerical calculation and simulation efficiency.At the same time,it also confirms the rationality of the GARCH model in option pricing research.The EGARCH model is more suitable for simulation than the other two models.Option price,its predicted value is closer to the real price.