Pricing Compound Options In The Two-factor Stochastic Volatility Jump-diffusion Model

Option pricing has been one of the core issues in field of financial mathematics and fi-nancial engineering.With the rapid development of financial markets,financial companies and investors,which love for complex financial derivatives,many financial institutions continuously introduce new derivatives,therefore,the new option(also amazing exotic option)appears and de-velops rapidly.Compound option is one of the most common and widely used exotic options.Compound option is the option of options,so it has two maturity and two executive price.Because under the influence of two different maturity,compound options are more sensitive to volatility by compared with the standard options and the value judgment is more complex.However,in the com-plex and volatile financial markets and the development of fast and slow economic environment,the traditional Black-Scholes model,jump diffusion model and single factor stochastic volatility model are no longer applicable,therefore,this paper presents a study of compound options under two factor stochastic volatility with the jump diffusion model.In this paper,from the perspective of multiple factors and fully consider that long and short risk caused by fluctuations in financial markets and the characteristics of economic development of fast and slow,we integrate the advantages of the jump diffusion model and stochastic volatil-ity model,we set up double factors jump diffusion stochastic volatility model.Under this model,firstly,we use the analysis method,such as Feynman-Kac theorem,Ito formula,the joint the char-acteristic function of multidimensional random variable and inverse discrete Fourier transform method,to derive the pricing formula of the standard European compound option.Through nu-merical examples comparison nine class model under the compound option price with the changes of S0,and analyzes the implied volatility of two different maturities,and the influence of the jump intensity and correlation coefficient of short-term and long-term volatility on the compound option price,we find that the model can better capture the time-varying characteristics of implied volatil-ity term structure,the correlation coefficient of short-term and long-term volatility has a positive impact on the compound option price,and the volatility of the option price is more intense in the short term volatility,the option price tends to be more stable in the long-term volatility.Secondly,we will stage single compound options to more compound option pricing in this model,The multiphase compound options pricing formula is derived by using the joint charac-teristic function of multidimensional random variables and the inverse Fourier transform method.In Merton model SVIJ model with TSVIJ model,we compared the price of the multiphase com-posite options through numerical example and analyzed the multiphase composite options under the influence of short-term volatility parameters,It is found that the addition of jump term and the stochastic volatility of two factors have a great influence on the pricing of multi period compound option,and the short-term volatility related parameters will have different impact on the price of the compound option.Therefore,in the actual financial market,investors should not only pay attention to long-term volatility,but also should pay attention to short-term volatility and its related parameters caused by the stock price volatility.In the two factor stochastic volatility jump diffusion model of compound option pricing is more suitable for the reality of the financial market.It provides a more powerful theoretical basis and method for the study of compound option pricing,and provides reference basis for risk managers to make more effective judgments.