Optimal Trading with a Trailing Stop
Applied Mathematics and Optimization, to appear, 2019
26 Pages Posted: 10 Jan 2017 Last revised: 21 Feb 2019
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: Suggested Citation