两个或多个几何平均价格的最小或最大值期权的定价

Pricing Options on th Minimum or Maximum of Two or Several Geometric Average Prices

两个或多个几何平均价格的最小或最大值期权是金融领域极具应用前景的新型复合期权.提出了一种新方法,简单而巧妙地得到了两个几何平均价格的最小值期权价格的解析公式.将该法直接推广,首次得到多个几何平均价格的最小和最大值期权的解析公式.首次给出的数值算例表明两个几何平均价格的最小值期权要比相应的最大值期权便宜,而它们都要比两资产的最大值期权便宜.若考虑红利率,则它们两者的价格都会减少.

The option on the minimum or maximum of two or several average prices is a kind of exotic compound options which has great applied prospects in the financial area. A new approach is developed in this paper to simply and skillfully obtain an analytical formula for the price of the option on the minimum of two geometric average prices. Furthemore, this method can be directly extended to price the options on the minimum and maximum of several geometric average prices and the according closed-form formulas are first derived. Numerical evidence is first given to show that the option on the minimum of two geometric average prices is cheaper than its counterpart maximum option and they are both cheaper than the option on the maximum of two assets. However, the prices of the options on the minimum and maximum of two geometric average prices will both decrease if dividends are considered.