Optimal Trading with a Trailing Stop

Applied Mathematics and Optimization, to appear, 2019

26 Pages Posted: 10 Jan 2017 Last revised: 21 Feb 2019

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Hongzhong Zhang

Columbia University

Date Written: February 18, 2019


Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing to buy and then sell an asset subject to a trailing stop. Under a general linear diffusion framework, we study an optimal double stopping problem with a random path-dependent maturity. Specifically, we first derive the optimal liquidation strategy prior to a given trailing stop, and prove the optimality of using a sell limit order in conjunction with the trailing stop. Our analytic results for the liquidation problem is then used to solve for the optimal strategy to acquire the asset and simultaneously initiate the trailing stop. The method of solution also lends itself to an efficient numerical method for computing the the optimal acquisition and liquidation regions. For illustration, we implement an example and conduct a sensitivity analysis under the exponential Ornstein-Uhlenbeck model.

Keywords: trailing stop, stop loss, optimal stopping, drawdown, stochastic floor

JEL Classification: C41, G11, G12

Suggested Citation

Leung, Tim and Zhang, Hongzhong, Optimal Trading with a Trailing Stop (February 18, 2019). Applied Mathematics and Optimization, to appear, 2019, Available at SSRN: https://ssrn.com/abstract=2895437 or http://dx.doi.org/10.2139/ssrn.2895437

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Hongzhong Zhang

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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