Abstract: When the foreign exchange rate is assumed to follow a continuous-diffusion process, we study the pricing of the geometric average Asian option and a new type of power option with an indicator function of the foreign exchange rate. In the empirical analysis, we utilize the actual market data of the foreign exchange rate of USD/CNY to obtain the values of the above options as well as Black-Scholes model. At the same time, the implied volatility of the related option is analyzed.

Key words: foreign exchange rate, geometric average Asian option, power option, empirical analysis

摘要： 在外汇汇率服从连续扩散过程模型下,研究了外汇汇率的几何平均亚式期权和附有汇率范围的示性函数的新型幂期权定价问题。在实证分析中,通过美元/人民币汇率的真实数据来计算以上所研究期权的价格,并和Black-Scholes模型下的期权定价进行比较,同时对相关期权的隐含波动率进行了分析。

关键词: 汇率, 几何平均亚式期权, 幂期权, 实证分析