Optimizing Mean-Reversion Trading Boundaries with First-Passage Times

Summary

This article develops a way to choose entry thresholds for a spread used in mean-reversion trading. A position is opened when the spread crosses an upper or lower boundary and closed when it returns to its mean. Tight boundaries create more trades with smaller minimum profit per trade; wider boundaries reduce trade frequency while raising that minimum. The proposed objective maximizes minimum total profit over a chosen period by balancing expected trade duration, waiting time between trades, and profit per trade.

The method estimates these times from mean first-passage times for a stationary AR(1) process. It fits the spread to that model, numerically approximates the relevant integrals, and searches a grid of candidate boundaries. A cointegrated pair example reports that out-of-sample results did not decay significantly, including during the coronavirus market crash. The evidence is limited: the approach assumes a stationary AR(1) spread, while real spreads may behave differently and remain outside thresholds for long periods. The author suggests rolling-window optimization as a possible way to adapt boundaries to changing regimes.

Key ideas

• Entry boundaries determine the tradeoff between trade frequency and minimum profit per trade.
• Mean first-passage times can estimate how long a spread takes to reach an exit or entry level.
• The optimization searches candidate boundaries to maximize estimated minimum total profit over a selected horizon.
• The numerical method assumes a stationary AR(1) spread, which may not capture real spread behavior.
• Rolling-window optimization may help boundaries adapt when market regimes change.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.