Statistical Arbitrage and Algorithmic Trading

Pairs trading strategy takes advantage of diversification across stocks, to produce a low-volatility investment strategy which is uncorrelated with the market. In this dissertation, we propose an OU-GARCH model to model the spread. We develop three trading strategies under GARCH volatility assumption. The first trading strategy is based on the percentile of spread, the second trading strategy maximizes the expected profit per-unit-time, and the third trading strategy maximizes the expected profit per-unit-time for a single trade given a finite investment horizon. Backtesting on both synthetic data and real daily data verifies the necessity of replacing constant volatility assumption with GARCH volatility assumption. OU-GARCH model plays the central role in this work. However, the key assumption for our OU-GARCH is that the spread needs to be mean-reverting and in reality, the mean reversion level can change after we open the trade, we then explore the calculation for adjusted optimal threshold when a single change point is detected after opening the trade. We also develop a trend-based trading strategy which is particularly suitable to be applied to the trending market condition.Doctor of Philosoph