基于EGARCH模型的远期开始期权定价

Forward-start options pricing based on EGARCH model

文章利用测度变换和期权定价的鞅方法,经过简单的数学推导得出了欧式远期开始期权的定价公式。选取了航天动力(600343)股票2010年交易日收盘价格的实际数据为样本建立了股票对数收益波动率的EGARCH模型,利用Eviews软件进行参数估计得到了波动率的方程,并对波动率进行了样本外预测,从而可以计算出比基于历史波动率更合理的期权价格。最后给出了一个远期开始看涨期权价格数值计算的例子。

By means of measure transformation and martingale method of option pricing, the pricing formulas of European forward-start options are obtained by the simple mathematical induction. Then the EGARCH model of the logarithm return volatilities is constructed by selecting the samples of real data of aerospace power stock （600343）~s daily transaction closing quotation price in 2010. The Eviews software is used to estimate the parameters and obtain the volatilities equation, The out-of- sample forecast of the volatilities is conducted, and the more reasonable options price than that based on historical volatilities is calculated. Finally, an example of numerical calculation of forward-start call options price is given.