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Theory of Brownian motion is often used to describe the random phenomena of chaos and disorder. This paper tries to make an empirical study on the price of foreign exchange by using theory of Brownian motion. First of all, we use the theory to establish a model to describe the behavior of foreign currency prices.Then the data of the Euro against the US dollar, the Australian dollar against the US dollar and Gold against the US dollar closing price per hour is introduced to simulate the exchange rate by using the model. Finally, we will use the simulated price and the actual price to do a comparative analysis, including the error range, motion direction and inflection point. It was found that the simulation and the actual exchange rate very similar, the results show that this model can be used to forecast. Introduction With the rapid development of the foreign exchange market, more and more investors enter into the spot market for speculation. Facing the numerous and complicated movements in the exchange rate, investors only by personal experience is difficult to accurately determine the exchange rate movements to make a correct decision buy or sale. In this paper the exchange rate was simulated by Brown motion model, in order to provide a more scientific basis for decision making for speculators. Foreign Studies on the Brownian motion is earlier, and widely used in the study of stocks, futures, gold and foreign exchange.In recent years, most people choose to use fractal Brownian theory. K. Ivanova , M. Ausloos used the data for six years to make a empirical analysis of exchange rate movements, it is proved that the exchange rate is more consistent with the multi fractal Brownian motion. S. V. Muniandy, S. C. Lim, R. Murugan used multi fractal Brownian motion model to do a empirical research on the influence of government’s intervention policies on the exchange rate in the foreign exchange market in Malaysia. Most of the research on foreign exchange in China is about the structure of foreign exchange investment, investment objects and investment strategies. As for the analysis of the exchange rate trend, Tan Weiping forecasted the trend through technology analysis. Zhang Yu studied four major exchange rates of China foreign exchange market, found that the exchange rate time series is nonlinear. In the nonlinear system, Liu Xing Quan, Wang Keyu use the fractional Brownian motion model to make empirical study about the US dollar against the yen in New York exchange market, found that estimates of H index values are in good agreement with the actual exchange rate fluctuations and trends. Previous studies show that exchange rate is in line with the Brownian motion, the time span of data is always in a few years and most choices is the fractal Brownian motion model. As a global speculative market the foreign exchange market is affected by many factors, investors use day trading to prevent the loss caused by the incident of second day. Therefore, in order to avoid the shortcomings of previous studies in this field we select 24 hours of exchange rate which is more in line with the characteristics of speculative foreign exchange market and more instructive to speculators. Fractal Brownian motion model denies the efficient market hypothesis and developed on the basis of geometric Brownian motion.The research scope of this paper is the closing price per hour of a single day which will rapid and sensitive response to information on the exchange market on the day.It is in line with the efficient market hypothesis that the price reflects all the information 3rd International Conference on Education, Management, Arts, Economics and Social Science (ICEMAESS 2015) © 2016. The authors Published by Atlantis Press 931 available. Therefore, this paper selects the geometric Brown motion model which can make this study more practical significance and application value. The Model of Brownian Motion The main factors of foreign exchange fluctuation are upward or downward trend and average volatility, The former depends on the length of time, the latter only depends on the random fluctuations caused by the movement of Brownian. We introduce a model describing the behavior of exchange rate: dst=μstdt+σstdwt (1) st is the foreign exchange price for t, dst is the changes in exchange rate, It shall be composed of certain items (expectation) and volatility (random), μ is the average exchange rate(expected drift rate), σ is standard deviation (volatility), wt is Standard Brownian motion. At time intervals Δt, Δwt~N(0,Δt),dwt=ε dt ,ε~N(0,1). According to Ito theorem: dlnst=(μ2 2  )dt+σdwt (2) That is dlnst~N[(μ2 2  )dt,σdt] . The discrete form of the stochastic differential equation can be expressed as: lnst+Δt-lnst=(μ2 2  )Δt+ σε t  (3) By (2) and (3) can be calculated: μ= t s s E t t t     ) ln (ln + 2 2  (4) σ2= t s s Var t t t     ) ln (ln (5) Empirical Analysis According to the different properties of foreign currencies, we select three currencies that are relatively stable and have different characteristics, including the safe haven currency and commodity currency. It can make data more representative.We chose closing prices per hour of the Euro against the US dollar, the Australian dollar against the U.S. dollar and Gold against the U.S. dollar of 24 hours in August 5, 2015. We take Δt is 1. According to historical data as well as formula (4), (5) calculate μ , σ, as table 1. Table 1 Estimating Means and Standard Deviations of Three Currencies EUR / USD AUD / USD Gold / USD  0.00016725985 ‐0.00010693263 ‐0.000035378392  0.001057341 0.001116575 0.001212112

Study on the Daily Exchange Rate Movement Based on the Model of Brownian Motion