外汇汇率波动的理论分析
Queueing theoretical analysis of foreign currency exchange rates
摘要：
我们提出了一个有用的方法来研究外汇汇率的统计特性。我们的方法是基于奖励理论，特别是所谓的更新奖励定理。对于索尼银行美元/日元（USD/JPY）汇率的第一次通过过程，我们评估了平均等待时间，该时间定义为客户在想要观察汇率的任何时刻（例如，当他们登录到计算机系统时）和下一次汇率变化之间必须等待的平均时间。我们发现，指数分布的第一次通过过程的假设应该被拒绝，Weibull分布似乎更适合解释的随机过程的索尼银行利率。我们的方法还使我们能够评估客户的预期回报，即可以预测客户必须等待多久，以及在他们登录计算机系统后，他们将在下一次价格变化时获得多少回报。我们通过与经验数据分析的比较来检验我们预测的有效性。
英文摘要：
We propose a useful approach for investigating the statistical properties of foreign currency exchange rates. Our approach is based on queueing theory, particularly, the so-called renewal-reward theorem. For the first passage processes of the Sony Bank US dollar/Japanese yen (USD/JPY) exchange rate, we evaluate the average waiting time which is defined as the average time that customers have to wait between any instant when they want to observe the rate (e.g. when they log in to their computer systems) and the next rate change. We find that the assumption of exponential distribution for the first-passage process should be rejected and that a Weibull distribution seems more suitable for explaining the stochastic process of the Sony Bank rate. Our approach also enables us to evaluate the expected reward for customers, i.e. one can predict how long customers must wait and how much reward they will obtain by the next price change after they log in to their computer systems. We check the validity of our prediction by comparing it with empirical data analysis.
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