基于不确定理论的风险中性测度及其在欧式期权定价中的应用

摘要

首先运用不确定理论推导了相应的不确定风险中性测度，修正了已有文献中涨跌期权不满足无套利原则的问题。然后将所得的风险中性测度用于欧式看涨和看跌期权的定价，并验证了涨跌期权价格之间的平价关系。最后研究了一类利差期权的定价问题，结合定义的风险中性测度给出了期权的定价公式。所推导的不确定风险中性测度与经典的无套利原则相吻合，而且考虑到了问题描述过程中存在的不精确性，弥补了单纯依赖随机理论的不足，可广泛地应用于金融衍生品的定价过程，为投资分析提供一定的理论依据。%Based on the uncertainty theory ,the corresponding uncertainty risk neutral measure was derived firstly by u‐sing the risk free rate ,which agrees with the no‐arbitrage principle .Then the established risk neutral measure was applied to price the European Call and Put options ,and the parity relationship was verified .Finally ,this paper gave the pricing formula for a Spread Option by the risk neutral measure .The derived risk neutral measure confirms the classical no‐arbitrage principle , takes into consideration the inaccuracy in the description process ,and makes up for the inadequacy of stochastic pricing theory , which can be widely used in financial derivatives pricing and provides the reliable theoretical basis for investment analysis .