Comparative Study Of Multivariate Levy Process In Option Market Applications

The multivariate modeling of financial assets has become more and more important in the modern financial market.such as multi-asset derivatives pricing,risk management of portfolio and optimal selection of portfolio.As a derivative security,the price of option is influenced by the change of underlying asset price.Due to the underlying asset price exists discontinuity,B-S model can not accurately depict the option price and introduce the Levy process with jump into the option market.With the rapid development of option on the innovation and the increasing range of exotic option,the structure of option is more complicated and the pricing of option is more and more difficult.Especially the underlying asset of option are multiple assets,namely multi-asset option.Therefore,we need to study the multidimensional method of Levy process.In this paper,aiming at the defect of B-S option price model,as well as the dimension disaster problem of pricing about multi-asset option or high-dimensional asset option,we discuss the complexities of option pricing calculation and other numerical methods and their advantages and disadvantages.Especially,we focus on the Monte Carlo Simulation method.A basket option and rainbow option are typical representatives of multi-asset exotic option.In this paper,Variance Gamma model of multidimensional Levy processes with jump be used to price a basket option and the second best options of rainbow options.Specific process is using a random time change technology,multivariate Variance Gamma model is modeled by time changed geometric Brownian motions with a common Gamma subordinator.Then the empirical analysis compared with the multivariate B-S model by Monte Carlo Simulation method.It is concluded that the result of multivariate Variance Gamma model is better than multivariate B-S model and more in line with realistic option market.