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应用风险偏好和均衡定价方法,考虑了标的资产服从分数布朗运动下的汇率期权定价问题.首先利用条件期望构建了条件过程的联合密度函数,然后,基于历史有限信息推导出分数欧式汇率期权的闭式解.为了理解定价模型,进一步分析了赫斯特指数对定价结果的影响.最后,给出了基于GBP/USD期权的实证研究.不同模型的结果说明了汇率市场具有分形特性.
Applying the risk preference and the equilibrium pricing method, we consider the pricing problem of the exchange rate option subject to the fractional Brownian motion under the underlying asset.Firstly, we construct the joint density function of the conditional process using the conditional expectation, and then deduce the closing of the fractional European exchange rate option based on the historical limited information In order to understand the pricing model, the influence of the Hurst Index on pricing results is further analyzed.Finally, an empirical study based on GBP / USD options is given.The results of different models show that the exchange rate market has the fractal character.