Optimal Pair-Trade Closing with Jumps in an Ornstein–Uhlenbeck Spread

Summary

This paper studies when to close a pair trade whose spread is modeled as an Ornstein–Uhlenbeck-type process driven by a finite-activity Lévy process. The jump component extends a setting where the asset difference is modeled without jumps, allowing the closing problem to account for discontinuous changes in the spread. The focus is on formulating the exit decision as an optimal stopping problem.

The authors prove a verification theorem and analyze a numerical method for the resulting free-boundary problem. They also establish rigorous error estimates and use numerical simulations to draw conclusions. The document summary does not give the form of the optimal boundary, the jump assumptions in detail, or specific simulation findings, so it offers no direct guidance on parameter selection or practical performance after trading costs.

Key ideas

• The pair trade holds one asset long and another short, with the asset difference serving as the modeled spread.
• The spread follows an Ornstein–Uhlenbeck-type process with finite-activity jumps.
• Closing the trade is framed as an optimal stopping problem.
• The study proves a verification result and analyzes a numerical free-boundary method.
• Error estimates support the numerical analysis, but the summary gives no specific boundary or performance figures.

Tags

# Optimal closing of a pair trade with a model containing jumps


# Optimal closing of a pair trade with a model containing jumps









A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely applied investment strategy in the financial industry. Recently, Ekström, Lindberg and Tysk studied the problem of optimally closing a pair trading strategy when the difference of the two assets is modelled by an Ornstein-Uhlenbeck process. In this paper we study the same problem, but the model is generalized to also include jumps. More precisely we assume that the above difference is an Ornstein-Uhlenbeck type process, driven by a Lévy process of finite activity. We prove a verification theorem and analyze a numerical method for the associated free boundary problem. We prove rigorous error estimates, which are used to draw some conclusions from numerical simulations.

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