OU Model Archives - Hudson & Thames

Optimal Trading Thresholds for the O-U Process

Front Page Research, Statistical Arbitrage

Pairs trading or statistical arbitrage is a famous strategy among institutional and individual investors since the 1990s. The concept behind this kind of strategy is straightforward. If the prices of assets move together historically, this tendency is likely to continue in the future. When the spread of the prices diverges from its long-term mean, one can short sell the over-priced stock, buy the under-priced one, and wait for the spread to converge to take the profit.

In general, to develop a pairs trading strategy, we need to solve two major issues, the first is how to select assets to form a process with mean reversion properties, and the second is how to decide when to trade…

Introducing: Arbitragelab Tear Sheets

Front Page Research, Statistical Arbitrage

Pairs selection is the first crucial step to building a pairs trading strategy. And it is no surprise, to perform it correctly, one must diligently examine, compare and contrast numerous test results, graphs and characteristics. For example, cointegration analysis alone can be performed in one of two methods – utilizing the Engle-Granger approach or the Johansen approach. To truly have the complete picture of the pairs suitability, with the Engle-Granger approach, the researcher should perform the test(and further analysis) for both possible combinations, A/B or B/A, in a pair since it is sensitive to which asset we choose to be the “dependent” one.
The Johansen test, in turn, provides multiple cointegration vectors, which also should be examined separately and taken into account. Not to mention the possible analysis of the residuals, auto-correlation tests, etc., brings even more data to the table for you to make your judgement.

And now, we have two options: memorize everything or constantly switch between numerous parameters and plots to check, contrast and compare. It results in loading your brain with tons of ‘noise’ that distracts from focusing on the evaluation itself. But it doesn’t have to be this way. Data analysis thrives when there is order, accessibility and clarity. And what embodies these three qualities better than combining everything into an interactive well-rounded tear sheet?

Pairs Trading with Stochastic Control and OU process

Front Page Research, Statistical Arbitrage

The concept of pairs trading is pretty straightforward. As described in [Gatev et al. (2006)], we first find two stocks that have moved together historically and then monitor the spread between these stocks. If the prices of the two stocks diverge, we short the winner and go long on the loser, hoping that these prices converge in the future. If the spread is mean reverting, it will revert to its historical mean. Then, the positions are reversed and a profit can be made.

There are various frameworks that could be used to identify a pair of stocks and build pairs trading strategies. In this article, we will be discussing a couple of papers related to stochastic control based approaches, which had the highest impact in this domain. We will not be discussing pairs selection techniques here, and interested readers can refer to the Stock Selection Methods using Copula and Machine Learning for Pairs Selection articles. The objective of these methods is to identify the optimal portfolio holdings in the legs of a pairs trade compared to other available assets. Stochastic control theory is used to determine value and optimal policy functions for this portfolio problem. It does sound a bit complicated, but, I’ll try to keep things simple and explain the intuition behind how and why these methods work.

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