Application of continuous-time random walk to statistical arbitrage

An analytical statistical arbitrage strategy is proposed, where the distribution of the spread is modelled as a continuous-time random walk. Optimal boundaries, computed as a function of the mean and variance of the first-passage time of the spread, maximises an objective function. The predictability of the trading strategy is analysed and contrasted for two forms of continuous-time random walk processes. We found that the waiting-time distribution has a significant impact on the prediction of the expected profit for intraday trading.