次分数布朗运动环境下最值期权定价

Pricing of Minimum or Maximum Option in Sub-Fractional Brownian Motion Environment

为了更贴合标的资产价格变化的实际过程,假设标的资产价格遵循由次分数Brown运动所驱动的随机微分方程,讨论次分数Brown运动环境下最值期权定价问题,利用次分数随机分析理论以及保险精算思想,获得次分数Brown运动环境下最值期权定价公式,并给出了数值算例,说明了市场不同的分形结构对期权价格的影响。

In order to better fit the actual process of price change of the underlying asset,it is assumed that the underlying asset price follows the stochastic differential equation driven by the sub-fractional Brownian motion,the maximum or minimum option pricing in the sub-fractional Brownian motion environment is discussed,and the price formula of the maximum or minimum option in the sub-fractional Brownian motion environment is obtained by the theory of sub-fractional stochastic analysis and the insurance actuarial method,and the numerical example is given to illustrate the influence of different fractal structures on the option price.