Option Pricing With Two-Factor Stochastic Volatility Jump-Diffusion Model

Due to the trend of financial globalization,market fluctuations will be violent due to various random factors,which also brings a lot of investment risks.As a relatively active financial derivative,options are widely used in hedging and risk management and play a positive role in increasing financial anti-risk capabilities and maintaining financial market stability.In the complex and changeable market environment,a reasonable option pricing model is particularly important.An option pricing model is the basis for option trading.Futhermore,the core of the option pricing model is volatility modeling.Therefore,establishing a more effective volatility model for option pricing is of great significance to the market.Based on this situation,this paper establishes a two-factor stochastic volatility jumpdiffusion model to explore the pricing problem of the option market,and analyzes the peak feature of the TFSVJD model.The feature can show that the model set in this paper can better show the peak and thick tail situation in the market.Then this paper applies the Girsanov theorem to transform the measure,and converts the TFSVJD model from the physical measure to the risk-neutral measure,which is also easier to analysis.After that,apply Feynman-Kac theorem and partial differential equation to calculate characteristic function and use Fourier inversion to derive option pricing formula,and extend to the derivation of iVIX and variance risk premium.Finally,numerical analysis and empirical application are carried out with Monte Carlo method.The TFSVJD model set in this paper adds the jump diffusion factor on the basis of the two-factor stochastic volatility,which can show the fluctuation of the volatility more completely,and adding the jump diffusion component to the volatility can better measure the market fluctuations.Determining the factors,in terms of numerical analysis,this paper verifies that the model in this paper has a higher volatility level and pricing level by comparing the original Heston model with the TFSVJD model in this paper,which also confirms the validity of the model in this paper.In addition,this article uses the SSE 50ETF option index launched in the Chinese market for numerical analysis and parameter estimation.Since the Chinese market is still developing and has a higher level of volatility,this article can show the significance of the TFSVJD model in the Chinese market from a practical perspective.