Research On European Option Pricing Under Mixed Gaussian Heston Stochastic Volatility Model

With the development of financial markets,options have been used by many investors and risk managers as derivatives.In particular,the continuous growth of volatility derivatives has put forward higher requirements for financial management.The B-S model is one of the most widely used models to study option pricing.But through historical data and empirical research show: firstly,its logarithmic returns do not follow the assumption of a standard normal distribution;secondly,it cannot well describe the characteristics of self-similarity and long-term dependence of assets.Therefore,in order to more accurately describe the changes in the price of the underlying asset,scholars choose to use the stochastic fluctuation model to characterize the underlying price of financial assets.The European option pricing and statistical simulation analysis are studied under the mixed Gaussian Heston stochastic volatility model.In the first part,mainly gets European option pricing under the mixed Gaussian Heston stochastic volatility model.First,the partial differential equation are obtains which satisfied the mixed Gaussian Heston stochastic stochastic model,then gets the existence and uniqueness of the solution of the volatility equation in the model,next discusses the theorem about the nature of the p-order moment of the solution,and the analytical solution of the mixed Gaussian Heston stochastic volatility model is finally obtained by combining the boundary conditions satisfied by the partial differential equation.In the second part,it is about the existence and uniqueness of the solution of the double mixed fractional Heston model,which is mainly applicable to the problem of fitting short-term options.The existence and uniqueness of the solution of the asset price equation of the double mixed-fraction Heston stochastic wave model are obtained,due to the complexity of its solution,Euler discretization is performed on the volatility and stochastic differential equations of stock prices in the model.In the third part,the 50 ETF options are selected for statistical simulation analysis.Perform descriptive statistical analysis on the selected data to verify characteristics such as the existence of agglomerations,thick tails,and asymmetry in the financial market,and estimate and sensitivity analysis of unknown parameters.Monte Carlo simulation method is used to analyze the effectiveness of the mixed Gaussian Heston stochastic volatility model.It shows that the mixed Gaussian Heston stochastic wave model is closer to its true value than the Heston model.The research results can provide more new basis for the theory and development of option pricing.