Research Of Option Pricing Based On Several New Stochastic Volatility Jump Models

In this dissertation,the transaction fee is introduced as a new variate into the stochastic volatility jump model to ascertain the relation between call option price and corrected volatility by using a probability method based on the pricing of European options,and the correction model of European call option pricing formula is acquired.Meanwhile,the influence of VIX option pricing is further studied by combining the logarithmic mean return stochastic volatility model with the logarithmic mean return jump model(which is named as logarithmic mean return stochastic volatility jump model),with methods of pricing and hedging the VIX options passing through the transform of Esscher and Fourier;then the formulas of both the pricing and hedging of VIX option are established.It also introduced a new model defined as the "4/2 stochastic volatility jump model",and build it through Lie symmetry theory and partial differential equation.The characteristic function of exponential logarithm and realized variance were obtained by the Fourier-laplace transformation.In addition,the pricing formula of SSE 50 ETF was received in view of this new model.Finally,the theoretical model built in this dissertation is verified by taking the latest underlying data of SSE 50 ETF options as a empirical example.The applicability of 4/2 stochastic volatility model,3/2 stochastic volatility model,as well as the classical Heston stochastic volatility model are compared by using the software of Excel,SPSS,MATLAB and Origin to analyze(process,calculate and fit)the research data.The results show that the option price defined as the 4/2 stochastic volatility jump model is more advantageous and can agreed well with the actual market price.