Stop-loss and leverage in optimal statistical arbitrage with an application to energy market

摘要

In this paper, we develop a statistical arbitrage trading strategy with two key elements in hi-frequency trading: stop-loss and leverage. We consider, as in Bertram (2009), a mean-reverting process for the security price with proportional transaction costs; we show how to introduce stop-loss and leverage in an optimal trading strategy.We focus on repeated strategies using a self-financing portfolio. For every given stop-loss level we derive analytically the optimal investment strategy consisting of optimal leverage and market entry/exit levels.First we show that the optimal strategy a la Bertram depends on the probabilities to reach entry/exit levels, on expected First-Passage-Times and on expected First-Exit-Times from an interval. Then, when the underlying log-price follows an Ornstein-Uhlenbeck process, we deduce analytical expressions for expected First-Exit-Times and we derive the long-run return of the strategy as an elementary function of the stop-loss. Following industry practice of pairs trading we consider an example of pair in the energy futures' market, reporting in detail the analysis for a spread on Heating-Oil and Gas-Oil futures in one year sample of half-an-hour market prices. (C) 2018 Elsevier B.V. All rights reserved.