Optimal Pairs Trading Cutoffs with Stochastic Volatility

Summary

The paper frames pairs trading as a choice among three positions: staying flat, holding one asset long and the other short, or reversing those positions. The spread between two correlated assets follows a mean-reverting process with stochastic volatility, and each position change incurs a fixed commission. The aim is to determine when switching positions is worthwhile after accounting for that cost.

The authors formulate the decision as an optimal switching problem and use viscosity-solution methods to establish existence and characterize cutoff points. Those cutoffs are obtained by solving quasi-algebraic equations, and numerical simulations illustrate the results. The document provides no specific simulation figures or empirical tests, so it does not show how the rules perform on market data. Its conclusions also depend on the assumed spread dynamics, transaction-cost structure, and model setup; practical use would require checking whether those assumptions fit the asset pair and trading environment.

Key ideas

• Pairs trading can be modeled as switching among flat, long-spread, and short-spread regimes.
• The spread is assumed to mean-revert while its volatility changes stochastically.
• A fixed commission on each trade affects when it is optimal to change positions.
• The proposed switching cutoffs are characterized through viscosity solutions and quasi-algebraic equations.
• Numerical simulations illustrate the analysis, but the document reports no empirical market validation.

Tags

# Optimal switching for pairs trading rule: a viscosity solutions approach


# Optimal switching for pairs trading rule: a viscosity solutions approach









This paper studies the problem of determining the optimal cut-off for pairs trading rules. We consider two correlated assets whose spread is modelled by a mean-reverting process with stochastic volatility, and the optimal pair trading rule is formulated as an optimal switching problem between three regimes: flat position (no holding stocks), long one short the other and short one long the other. A fixed commission cost is charged with each transaction. We use a viscosity solutions approach to prove the existence and the explicit characterization of cut-off points via the resolution of quasi-algebraic equations. We illustrate our results by numerical simulations.

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