﻿ 一种基于高频数据的汇市统计套利策略 A Statistical Arbitrage Strategy in Forex Market Based on High-Frequency Data

Finance
Vol.07 No.01(2017), Article ID:19565,9 pages
10.12677/FIN.2017.71005

A Statistical Arbitrage Strategy in Forex Market Based on High-Frequency Data

Dunjian Xiao1, Xiaowei Deng2, Bingqian Xia1

1Overseas Education College, Nanjing Tech University, Nanjing Jiangsu

2School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing Jiangsu

Received: Dec. 24th, 2016; accepted: Jan. 15th, 2017; published: Jan. 18th, 2017

ABSTRACT

In capital market, arbitrage is an essential trading method to avoid risks. Statistical arbitrage, which is a genre of arbitrage, has been widely utilized by foreign financial institutions since several decades ago. Since lacking of Short Hedge Mechanism, statistical arbitrage can hardly be realized in domestic capital markets. However, the situation is being relieved with the introduction of margin trading and stock index futures. And the trend to set up Short Hedge Mechanism is overwhelming. In this dissertation, we tested the arbitrage chances in forex market by adopting the thought of statistical arbitrage, combining with cointegration modeling and every minute’s closing rate of EUR/USD and CHR/JPY, which are highly correlated with each other, within 24 hours. After studying in the time series of price difference, we found that there were abundant opportunities for arbitrage. Hence, we are able to give out a novel quantified path for investors in the future.

Keywords:Statistical Arbitrage, High-Frequency Data, Cointegration Model, Forex Trading

1南京工业大学海外教育学院，江苏 南京

2南京工业大学数理科学学院，江苏 南京

1. 引言

1.1. 统计套利背景简介

1.2. 分析方法

2. 统计套利模型介绍

2.1. 模型含义概述

2.2. 统计套利不是无风险套利

2.3. 统计套利的数学定义

Hogan, Jarrow, Teo和Warachka (2004) [9] 对统计套利进行了精确的数学定义，他们强调统计套利是具有零初始成本、自融资的交易策略。

1)

2)

3)

4) 若

1) 零初始成本；

2) 利润的现值为正数，统计套利有条件地向纯套利收敛；

3) 亏损的概率趋近于0 (与无风险套利的不同之处在于，无风险套利亏损的概率等于0)；

4) 时间的平均方差趋近于0。

Figure 1. Curve: decision of entering the market

3. 实证分析

3.1. 选取配对货币对(相关性检验)

3.3. 协整检验

Figure 2. Scatter plot of X1

Figure 3. Scatter plot of X5

3.4. 套利机会检验与进场出场点设置

3.4.1. 建立交易组合

3.4.2. 确定交易信号

Figure 4. Price difference after decentralization

3.4.3. 设定建仓、平仓与止损阈值

4. 样本外绩效检验

5. 不足与改进

Figure 6. Efficiency test outside sample data

6. 总结与展望

A Statistical Arbitrage Strategy in Forex Market Based on High-Frequency Data[J]. 金融, 2017, 07(01): 38-46. http://dx.doi.org/10.12677/FIN.2017.71005

1. 1. Levich, R.M. (2001) International Financial Markets. McGraw-Hill/Irwin, New York, 141-152.

2. 2. Bolland, P.J. and Connor, J.T. (1998) A Robust Non-Linear Multivariate Kalman Filter for Arbitrage Identification in High Frequency Data. Neural Networks in Financial Engineering, 122-135.

3. 3. Engle, R.F. and Granger, C.W.J. (1987) Co-Integration and Error Correction: Representation, Estimation, and Testing. Econometrica, 55, 251-276. https://doi.org/10.2307/1913236

4. 4. Burgess, N. (2000) Statistical Arbitrage Models of the FTSE 100. Computational Finance, The MIT Press, Cambridge, 297-312.

5. 5. Rudy, J., Dunis, C., Giorgioni, G. and Laws, J. (2010) Statistical Arbitrage and High-Frequency Data with an Application to Eurostoxx 50 Equities. Social Science Electronic Publishing, Rochester.

6. 6. 方昊. 统计套利的理论模式及应用分析: 基于中国封闭式基金市场的检验[J]. 统计与决策, 2005(12): 14-16.

7. 7. 仇中群, 程希骏. 基于协整的股指期货跨期套利模型[J]. 系统工程, 2008(12): 26-29.

8. 8. 叶恒洁. 基于协整的统计套利实证研究[J]. 中国商贸, 2009(13): 238-238.

9. 9. Hogan, S., Jarrow, R., Teo, M. and Warachka, M. (2004) Testing Market Efficiency Using Statistical Arbitrage with Applications to Momentum and Value Strategies. Journal of Financial Economics, 73, 525-565. https://doi.org/10.1016/j.jfineco.2003.10.004

10. 10. Vidyamurthy, G. (2004) Pairs Trading: Quantitative Methods and Analysis. Pearson Schweiz Ag, Zug, 35-47.