Optimal switching for pairs trading rule: a viscosity solutions approach

TL;DR

This paper develops a mathematical framework using viscosity solutions to determine optimal switching thresholds in pairs trading strategies involving assets with mean-reverting spreads and stochastic volatility.

Contribution

It introduces a novel viscosity solutions approach to explicitly characterize optimal switching thresholds in a complex stochastic environment.

Findings

Explicit cut-off points are derived via quasi-algebraic equations.

Numerical simulations demonstrate the effectiveness of the proposed method.

The model accounts for transaction costs and stochastic volatility effects.

Abstract

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.