Research On Statistical Arbitrage Based On O-U Process

Statistical arbitrage is one kind of market neuter strategy without regard of market trend. This strategy can gain more stable earnings under lower investment risk which is only suit for market with short mechanism and long mechanism. At the beginning of this year, stock-index futures and margin trading are set up in domestic capital market. With the development of short mechanism in domestic stock market, statistical arbitrage will get more extensive application.Before Statistical arbitraging, we should choose a pair of related stocks or other assets in high dependent, and then based on statistical analysis of the historical data, including unit root test and cointegration test, we construct cointegration model between this two stocks as a portfolio. We can get residual time series thought cointegration model. We assume that the sequence has the characteristics of mean reversion, it means when the price difference sequence drift apart from mean, there exists an arbitrage opportunity, we built a long or short position. Then we close the position until the price difference sequence move back to mean. We get benefit in this way. But in the case of the spread apart from mean in long distance, we also should close position to control loss. The trading signal is important which control when building position, when close position, when stop loss. As spread has the characteristics of mean reversion, the arbitrage will be profitable. The statistical arbitrage will be efficient by automation control system.There are much domestic and foreign research on trading signal. We could model trading signal by GARCH method and neural network and so on, these methods have their advantages and disadvantages. The spread have the characteristics of mean reversion, at the same time, the Ornstein-Uhlenbeck process, one of the stochastic differential equation, is suitable to describe mean reversion spread, so we assume that the spread conforms to Ornstein-Uhlenbeck process. We discussed two kinds of situations, one is maximizing expected profit function, the other one is maximizing Sharpe value. We solve the optimal trade signals by maximizing these two kinds of objective function. As the first situation is relatively simple, we pay more attention on the first situation and solve out the trading signal's approximate analytic solution. We mainly used the analytic solution in empirical part. We can get more accurate numerical solution of each conditions.Considering the traditional statistics arbitrage method are instability, existing mismatch problem of internal sample model and outside sample data, this paper presents a dynamic statistical arbitrage, that means model parameters and optimal trading signal will be updated with the updating data, avoiding mismatching problem. This paper gives case analysis by four bank shares data in Chinese stock market. Firstly, comparing the dynamic statistical arbitrage and traditional statistical arbitrage through yields, transaction times, transaction success rate and so on, we found dynamic method gains more stable profit, more arbitrage opportunities and higher trading success rate. This paper compare dynamic statistical arbitrage with the 2008 bear market and 2009 bull market respectively. Through beta coefficient we obtained that dynamic statistical arbitrage have market neutral features. Through cumulative yield, volatility and Sharpe index value, we obtained that dynamic statistical arbitrage is more stable than stock market.