亚式期权是一种重要的金融衍生工具,它是金融市场最受欢迎的路径依赖型期权之一,其收益取决于期权整个周期内标的资产的平均价值.由于风险的动态不确定性,因此假设外汇市场中的利率是一个不确定过程,其变化规律可由不确定微分方程来刻画.为了对冲外汇市场中的风险,银行拟定一个合同来赋予投资者以敲定价格购买外汇的权力,而拥有这项权利需要付出一定的代价.因此,本文以不确定外汇模型为基础研究了亚式期权问题,结合不确定理论和公平定价原则最终推导了几何平均亚式期权的定价公式.
Asian option is a significant financial derivative instrument, which is one of the most popular path-dependent options. Its income is decided by the average value of underly asset within the whole lifetime of the option. Influenced by the dynamic uncertainty of risk, the interest rate in foreign exchange market is assumed to be modeled by uncertain process and its law of change obeys an uncertain differential equation. In order to hedge against risks from the foreign exchange market, the bank provides a contract for investors to give them a kind of right instead of obligation to buy foreign exchange at a knock exchange rate. Naturally, for possessing such right, the investor needs to pay for the contract. Hence, based on the uncertain foreign exchange model, this paper studies the Asian option problem. Combining uncertainty theory and fair price principle, the pricing formulas of geometric average Asian option are deduced.
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