Optimal Trading with a Trailing Stop

Zhang Hongzhong

Chapter 9 in Stochastic Drawdowns, 2018, pp 203-223 from World Scientific Publishing Co. Pte. Ltd.

Abstract: Trailing stops are a popular trade order widely used by proprietary traders and retail investors to provide downside protection for an existing position. A trailing stop is triggered when the prevailing price of an asset falls below a stochastic floor, which is often a percentage of the running maximum. In contrast, a limit sell order can be considered as a selling order that is triggered when the asset price reaches some target. Whether an asset holder should passively wait until a trailing stop is triggered or sell the asset more aggressively with a limit sell order is a question that remains open. In Chapter 9, we address this question by deriving the optimal trading strategy when a trailing stop is imposed. We develop an analytical tractable framework with linear diffusion models, and identify the early exercising premium that an asset holder can get by trading aggressively. Our approach is to first derive some key technical results by solving an auxiliary optimal trading problem with a fixed stop-loss level. Then, we study the optimal exit strategy for selling the asset no later than the trailing stop, and prove that the early exercising premium is maximized when a limit sell order is placed in conjunction with the trailing stop. In order words, an asset holder should only trade passively if the key price target is not reached; otherwise, an immediate sell is optimal and better than waiting for the trailing stop. Different from the variational inequality approach we used in Chapter 8, our solution method is to demonstrate that a proposed stopping rule yields strictly positive “time value”, then prove that the optimal continuation region cannot be larger than the one in the proposed stopping rule. Moreover, we also study the optimal entrance strategy for purchasing this asset and setting up the trailing stop. Using an exponential Ornstein–Uhlenbeck (OU) model, we numerically demonstrate our optimal trading strategy, and show that the optimal entrance region is of the form (0, A), while the optimal exit region is (B, ∞) for 0 Keywords: Drawdown; Maximum Drawdown; Insurance; Optimal Trading (search for similar items in EconPapers)
JEL-codes: C02 G32 (search for similar items in EconPapers)
Date: 2018
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