随机利率下基于Tsallis熵及O-U过程的幂式期权定价

摘要

为了准确描述股票价格的变化规律,对经典的Black-Scholes期权定价模型进行改进,利用具有尖峰厚尾和长期相依特征的Tsallis熵分布、具有均值回复性的O-U过程,建立股票价格的变化模型,在无风险利率服从Vasicek模型下,运用随机微分和等价鞅测度的方法得到了幂式期权的定价公式,推广了经典的Black-Scholes定价理论,扩展了已有文献的结论.%The classical Black-Scholes option pricing model was improved in order to accurately describe the fluctuation of stock price.Thus,the distribution of Tsallis entropy,which had fat-tailed and long-term dependent characteristics,and O-U process were selected to describe the law of the stock prices fluctuation.By using the stochastic differential and martingale under the Vasicek interest rate model,the pricing formulas of power European options were obtained.The formulas not only generalized the classical Black-Scholes conclusion,but also corroborated the conclusions in the other literature.