基于长记忆性特征的欧式期权模糊定价研究

Fuzzy pricing of European option based on the long-term memory property

为了将金融市场的长记忆性特征纳入到不确定环境下欧式期权定价研究中,用分数布朗运动去刻画标的资产价格的变化过程.在分数Black-Scholes模型的基础上,考虑到金融市场的不确定性包括随机性和模糊性,运用随机分析、分形理论和模糊集理论构建了不确定环境下金融市场长记忆性特征的欧式期权定价模型.其次,分析了金融市场长记忆性的度量指标Hurst指数H对欧式期权定价的影响.最后,通过数值实验论证了该定价模型的合理性和可行性.研究结果表明:在不确定环境下充分考虑长记忆性特征得到的欧式期权定价模型更符合金融市场.

In order to introduce the long memory property of financial markets into the study of European option pricing under uncertain environment,the fractional Brownian motion is used to describe the dynamics of the underlying stock price.On the basis of fractional Black-Scholes model,considering that the financial market is uncertain with randomness and fuzziness,using stochastic analysis,fractal theory and fuzzy set theory to construct European option pricing model based on the long-term memory property of the financial market in a uncertain environment.Then the influence of Hurst index H,a measure of long-term memory in financial market,on European option pricing is analyzed.Finally,numerical experiment demonstrates the proposed pricing model are reasonable and acceptable.The results show that the pricing model of European options with long-term memory property is more suitable for financial market under uncertain environment.