基于混合次分数布朗运动环境下的欧式障碍期权定价

Pricing of European Barrier Options Based on Mixed Sub-Fractional Brownian Motion Environment

研究了基于混合次分数布朗运动环境下的欧式障碍期权的定价问题.考虑原生资产连续支付红利,运用Δ-对冲原理得到欧式下降敲出看涨障碍期权的显式解,以及欧式障碍期权看涨-看跌平价公式.最后进行数值模拟,通过控制变量法,研究了Hurst指数H、初始标的资产价格S、敲定价格K、障碍值SB、无风险利率r、红利率q、波动率σ对期权价格的影响.与混合分数布朗运动相比,混合次分数布朗运动能更好地刻画金融资产价格的变动,因此本文得到的混合次分数布朗运动环境下欧式障碍期权定价公式更符合金融市场规律.

In this paper,we study the pricing problem of European barrier options based on a mixed sub-fractional Brownian motion environment.In this paper,we consider the continuous dividend payment of the primary asset and apply the-hedging principle to obtain the explicit solution of the European down-and-out call barrier option and the European callput parity formula of the barrier option.Finally,numerical simulations are conducted to investigate the effects of the index H,the initial underlying asset price S,the strike price K,the barrier S_B,the risk-free rate r,the dividend rate q,and the volatilityσon the option price through the control variables method.Compared with the mixed fractional Brownian motion,the mixed sub-fractional Brownian motion can better portray the movement of the financial asset price.So the European barrier option pricing formula obtained in this paper in the mixed sub-fractional Brownian motion environment is more consistent with the financial market laws.