Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs

TL;DR

This paper develops an optimal trading strategy framework under exponential Ornstein-Uhlenbeck price dynamics with transaction costs, analyzing entry and exit timing through double stopping and switching problems, supported by numerical illustrations.

Contribution

It introduces a combined analysis of double stopping and switching problems for optimal trade timing under mean-reverting prices with fixed costs, revealing conditions for strategy equivalence.

Findings

Optimal entry generally occurs at low prices.

Waiting can be optimal when prices are near zero.

The continuation region for entry can be disconnected.

Abstract

This paper studies the timing of trades under mean-reverting price dynamics subject to fixed transaction costs. We solve an optimal double stopping problem to determine the optimal times to enter and subsequently exit the market, when prices are driven by an exponential Ornstein-Uhlenbeck process. In addition, we analyze a related optimal switching problem that involves an infinite sequence of trades, and identify the conditions under which the double stopping and switching problems admit the same optimal entry and/or exit timing strategies. Among our results, we find that the investor generally enters when the price is low, but may find it optimal to wait if the current price is sufficiently close to zero. In other words, the continuation (waiting) region for entry is disconnected. Numerical results are provided to illustrate the dependence of timing strategies on model parameters and transaction costs.