Discussion On Several New Methods Of Program Trading

With the development of the computer science technology, program trading has be-come more and more popular, which leads more researchers focusing on it. In this paper, we mainly discuss about program trading strategies. Based on the number of the financial products used, we do research about trading strategies by using two products and single product respectively. For two financial assets, we consider building a model to match two stock price trends and design a statistical arbitrage strategy based on cross-correlation analysis. For the single asset, we focus on the timing strategies based on stationary process.Before using statistical arbitrage strategies, the investors need to find the financial products to be used by matching their price trends. To solve this problem, the most com-mon methods nowadays are based on machine learning and pattern recognition. However, these algorithms deeply rely on the sample data in order to get a good model, which cause the problem that the model is irreproducible. In the first part, we design an image matching algorithm to recognize the stock price trends by computer automatically based on Monge problem. In Monge problem, we can find the optimal transportation plan to move two mounds and compute the minimum energy. Two stock price trends can be considered as two mounds. When the matching degree is high, the energy of the optimal transportation plan will be low, which can be used as matching rule. The advantage of this model is that it doesn’t depend on historical data anymore. Since the original prob-lem is used to compute the real transportation energy, Euclidean distance is considered in the mathematical model. To improve the discrimination of the result of price-matching, we propose|·|p distance to match the stock price trends. We calculate the variation form to get a quasilinear elliptic partial differential equation with unknown H(x,y) To solve this model, we design an algorithm based on its symmetry. Then, we use this al-gorithm to match the stock price trends of China Life Insurance, China Pacific Insurance, Citic Securities and Leshi Internet Information & Technology Corp. From the results, we conclude that the stock prices of China Life Insurance and China Pacific Insurance, both in the same industry, match closest. Moreover, the match degree of China Pacific Insur-ance and Leshi Internet Information & Technology Corp is worst. Meanwhile, comparing the matching results with the Euclidean distance, we find the discrimination has been improved with the increase of p.In the second part, we discuss about the statistical arbitrage strategy between future markets and spot markets. And we design an arbitrage strategy based on cross-correlation between Chinese treasury futures contracts and treasury ETF. Firstly, we find significant cross-correlation between these two return series by Qcc test. We further discuss the relationship using the DCCA coefficient and DCCA method between the price series. And we show that the cross-correlation is long range. For price series{xt} and{yt}, we used the linear model xt-βtyt=αt+ut to design an arbitrage algorithm. In some researches, they estimate the parameters using the least square method. However, based on the cross-correlation we can use DFA regression method to build a new arbitrage strategy which has stable return. We can get the conclusion that the trading result based on the DFA regression has better return than the least square method. It is a new approach to investigate the statistical arbitrage by using cross-correlation.In the third part, we mainly focus on the strategies using single financial asset. Ac-cording to the stationary trading theory proposed in Wang and Zheng [112], we get the conclusion that under the assumption that the increment of logarithmic price is strong stationary if we trade using the signals generated from a strong stationary process, with the increase of trading times, the mean logarithmic return will converge almost surely. When the mean logarithmic return converges to a positive number, the accumulate log-arithmic return will increase stably. Based on this theory, we use technical indictors to build stationary processes. Firstly, we use a single time scale stationary technical indictor to design a trading strategy which has stable return. Secondly, we propose the multi-time scale model and use a stationary process based on MACD in the multi-time scale to get a new strategy; which can combine the advantage of long-time scale and short-time scale. After testing the historical data, we find that the Sharp ratio of this strategy is 3.07 and the yearly return is 42.8%. And the mean logarithmic return converges with the increase of trading times. Then, we add the volume information into the strategy by using two dimensional stationary process to filter the false signals, which improves the Sharp ratio. Finally, we use machine learning method to design the trading strategy, which can adapt to the market automatically. We get a black box model by inputting historical stationary indicators and using simple linear model. Then, we apply it to trade on the out-of-sample data. This strategy based on machine learning method also has stable return, while the mean logarithmic return converges. What we discuss in this part is innovative in theory and important in practice.