基于Levy过程的彩虹期权定价探讨

金融资产的多元模型在现代金融市场中越来越普遍,且已被应用在许多领域,如多资产衍生品定价、投资组合的风险管理和最优投资组合选择等。因此,Levy过程多维化方法值得研究。彩虹期权是一类多资产期权。运用多维Levy过程中的多元Variance Gamma模型,对彩虹期权中的择次好期权进行定价。具体过程为使用随机时钟变化技术,通过一个共同的Gamma从属过程时变几何布朗运动建立多元Variance Gamma模型。并进行实证分析,与多元Black Scholes模型进行比较,得出多元Variance Gamma模型的结果稍高,更加符合现实市场,并且多元Variance Gamma模型引入了跳,能更加贴切地描述现实市场。因此,将Levy过程多维化来解决多资产期权定价问题具有创新性,能对金融市场中多资产期权更精准地定价。

The multivariate modeling of financial assets has become more and more common in the modern financial market, which are widely used in many fields, such as multi-asset derivatives pricing, risk management of portfolio and optimal selection of portfolio. So, the study of muhidimensional method of Levy process is necessary. Rainbow options are a kind of multiasset options. Multivariate Variance Gamma model of multidimensional Levy processes can be used to price the second best options of rainbow options. Specific process is using a random time change technology, and multivariate Variance Gamma model is modeled by time changed geometric Brownian motions with a common Gamma subordinator. Then the empirical analysis is compared with the Black Scholes model. It is concluded that the result of multivariate Variance Gamma model is slightly higher and more in line with realistic market. And the multivariate Variance Gamma model with jump is more appropriate to describe the real market. It is innovative to solve the problem of multi-asset option pricing of using the multidimensional Levy process. It can be more accurate pricing for multi-asset options in the financial market.