Mean Reversion Trading with Sequential Deadlines and Transaction Costs

TL;DR

This paper develops a mathematical framework for optimal trading strategies in mean-reverting markets with finite entry and exit deadlines, considering transaction costs and multiple trading strategies.

Contribution

It introduces a unified approach to solve optimal double stopping problems for various mean-reverting models using local time-space calculus.

Findings

Derived nonlinear integral equations for trading boundaries

Provided numerical examples of optimal trading strategies

Analyzed three different trading strategies with finite deadlines

Abstract

We study the optimal timing strategies for trading a mean-reverting price process with afinite deadline to enter and a separate finite deadline to exit the market. The price process is modeled by a diffusion with an affine drift that encapsulates a number of well-known models,including the Ornstein-Uhlenbeck (OU) model, Cox-Ingersoll-Ross (CIR) model, Jacobi model,and inhomogeneous geometric Brownian motion (IGBM) model.We analyze three types of trading strategies: (i) the long-short (long to open, short to close) strategy; (ii) the short-long(short to open, long to close) strategy, and (iii) the chooser strategy whereby the trader has the added flexibility to enter the market by taking either a long or short position, and subsequently close the position. For each strategy, we solve an optimal double stopping problem with sequential deadlines, and determine the optimal timing of trades. Our solution methodology utilizes the local time-space calculus of Peskir (2005) to derive nonlinear integral equations of Volterra-type that uniquely characterize the trading boundaries. Numerical implementation ofthe integral equations provides examples of the optimal trading boundaries.