Optimal Trading Stops and Algorithmic Trading

Trading stops are often used by traders to risk manage their positions. In this note, we show how to derive optimal trading stops for generic algorithmic trading strategies when the P&L of the position is modelled by a Markov modulated diffusion. Optimal stop levels are derived by maximising the expected discounted utility of the P&L. The approach is independent of the signal used to enter the position. We analyse in details the case of trading signals with a limited (random) life. We show how to calibrate the model to market data and present a series of numerical examples to illustrate the main features of the approach.