中文摘要：

主要研究变系数Black-Scholes模型有红利支付下的欧式期权定价的估计问题.首先,构造了波动率函数的估计量,并讨论了所得估计的强收敛性、渐近正态性和收敛速度.然后,基于波动率函数的估计,利用期权定价公式得到了变系数Black-Scholes模型有红利支付下的欧式期权价格的估计.最后,证明了所得估计量是期权价格的强相合估计.

英文摘要：

The estimation of European pricing options on dividend-paying stocks for Black-Scholes models with time-varying coefficients was studied. Firstly, the estimation of the volatility function of our models was proposed, and the strong convergence, asymptotic normality and convergence rate of the estimation were discussed. Secondly, based on the estimation of the volatility function, the estimation of European pricing options on dividend-paying stocks for Black-Scholes models with time-varying coefficients was obtained by using the pricing formula for European options. Finally, the strong consistency of the estimation of the pricing option was proved.