Pairs Trading with Hidden Drift Regimes and Volatility-Penalized Utility

Summary

The document formulates pairs trading as a dynamic portfolio optimization problem. The spread between two related securities follows a Gaussian mean-reverting process, while its drift rate changes according to an unobserved finite-state continuous-time Markov chain. Because the regime is hidden, the authors use stochastic filtering to convert the partial-information problem into a full-information formulation. They solve the resulting problem for logarithmic utility and include a terminal wealth penalty tied to realized portfolio volatility.

The work characterizes optimal dollar-neutral strategies and value functions under both full and partial information. It also reports that certainty equivalence holds for the optimal strategy, meaning the strategy can be characterized using the filtered estimate of the hidden state. A numerical illustration uses a two-state Markov chain, but the document provides no empirical market validation or evidence of profitability. The results are therefore theoretical and depend on the assumed spread dynamics, filtering model, utility choice, and volatility-based penalty.

Key ideas

• The asset spread is modeled as a Gaussian mean-reverting process with hidden Markov drift regimes.
• Stochastic filtering reduces the partial-information optimization problem to a full-information form.
• The objective uses logarithmic utility and penalizes terminal wealth according to realized volatility.
• Optimal dollar-neutral strategies are characterized for full and partial information.
• A toy two-state example illustrates the model, with no real-market performance evidence reported.

Tags

# Pairs Trading under Drift Uncertainty and Risk Penalization


# Pairs Trading under Drift Uncertainty and Risk Penalization









In this work, we study a dynamic portfolio optimization problem related to pairs trading, which is an investment strategy that matches a long position in one security with a short position in another security with similar characteristics. The relationship between pairs, called a spread, is modeled by a Gaussian mean-reverting process whose drift rate is modulated by an unobservable continuous-time, finite-state Markov chain. Using the classical stochastic filtering theory, we reduce this problem with partial information to the one with full information and solve it for the logarithmic utility function, where the terminal wealth is penalized by the riskiness of the portfolio according to the realized volatility of the wealth process. We characterize optimal dollar-neutral strategies as well as optimal value functions under full and partial information and show that the certainty equivalence principle holds for the optimal portfolio strategy. Finally, we provide a numerical analysis for a toy example with a two-state Markov chain.

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