Stop loss and leverage in optimal statistical arbitrage with an application to energy market
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.
Energy Economics