模糊随机环境中的欧式障碍期权定价

摘要

Considering that the real world is uncertain with fuzziness and randomness, stochastic analysis and fuzzy set theory are employed to study the pricing of European barrier options in fuzzy and stochastic environments. Since the methods used to price all kinds of European barrier options are almost the same, the paper only takes European up-and-out call options as an example to illustrate. By assuming that the underlying asset price follows a fuzzy stochastic process, the call barrier option's fuzzy price and the pricing formula in the sense of possibility mean value are derived.%考虑到现实世界的不确定性包含随机性和模糊性,运用随机分析和模糊集理论研究了模糊随机环境中的欧式障碍期权定价问题.由于各种欧式障碍期权的定价方法和思路基本相同,因此仅以向上敲出看涨障碍期权为例说明如何定价.通过假设标的资产价格服从模糊随机过程,得到了向上敲出看涨障碍期权的模糊价值和其在可能性均值意义下的定价公式.