基于混合分数布朗运动下欧式障碍期权的模糊定价研究

Fuzzy Pricing of European Barrier Options Based on Mixed Fractional Brownian Motion

金融市场经常受到一些不确定因素的影响,使得障碍期权的定价具有模糊性,同时资产价格的变化具有长记忆性和“尖峰厚尾”的特征.本文将金融市场的长记忆性特征纳入到模糊环境下的欧式向下敲出看涨障碍期权定价模型中,用混合分数布朗运动刻画资产价格的变化过程.通过引入三角直觉模糊数来刻画期权价格估计的不确定性,构建了在混合分数布朗运动下的Black-Scholes模型下欧式向下敲出看涨障碍期权的定价模型,给出了障碍期权三角直觉模糊价格截集.重点研究了长记忆性指标Hurst指数H对期权价格的影响,通过数值实验对模型的灵敏性和稳健性进行了分析,结果表明:在模糊环境下考虑长记忆性特征所得到的欧式向下敲出看涨障碍期权定价模型更符合金融市场.

The financial market is often affected by some uncertain factors,which makes the pricing of barrier option fuzzy.Meanwhile,the motion of asset prices usually exhibits long memory and heavy tails.The long memory characteristics of financial markets are incorporated into the pricing model of the European down-and-out call barrier option under fuzzy environment,and the process of asset price fluctuations is described by the mixed fractional Brownian motion.By introducing the triangle intuitionistic fuzzy number to describe the uncertainty of option price estimation,a pricing model of European knock out barrier option based on the Black-Scholes model under mixed fractional Brownian motion is constructed,and the triangle intuitionistic fuzzy price cut-off set of barrier option is given.The paper also focuses on the effect of the Hurst index H on the option price.The sensitivity and robustness of the model are analyzed by numerical experiments.The results show that the European down-and-out option pricing model with long memory is more reasonable with the financial market.