Statistical arbitrage trading strategies allow agents to generate profits by taking advantage of (typically short lived) predictability in the direction of prices or other state variables. In this talk, we will introduce two classes of such strategies that incorporate very different kinds of information from the limit order book (LOB).

In the first part of the talk, we develop a trading strategy that employs limit and market orders in a structurally dependent multi-asset economy, e.g., options, futures and stocks. To model the structural dependence, the midprice processes follow a multivariate reflected Brownian motion on the closure of a no-arbitrage region which is dictated by the assets' bid-ask spreads. We pose and solve a stochastic optimal control problem for an investor who takes positions in these assets and we will explore the key features of the resulting strategies and their simulated profit and loss. 

In the second part of the talk, we use high-frequency data from the Nasdaq exchange to build a measure of volume order imbalance in the LOB. We show that our measure is a good predictor of the sign of the next market order (MO), i.e. buy or sell, and also helps to predict price changes immediately after the arrival of an MO. Based on these empirical findings, we introduce and calibrate a Markov chain modulated pure jump model of price, spread, LO and MO arrivals, and order imbalance. As an application of the model, we pose and solve a stochastic control problem for an agent who maximizes terminal wealth, subject to inventory penalties, by executing roundtrip trades using LOs. We demonstrate the efficacy of the model and optimal control problem by calibrating the model and testing its performance on out-of-sample data. We show that introducing our volume imbalance measure into the optimisation problem considerably boosts the profits of the strategy.

[ This talk is based on joint work with Álvaro Cartea, Ryan Donnelly and Jason Ricci: Enhancing Trading Strategies using Order Book Signals (http://ssrn.com/abstract=2668277) and Trading Strategies within the Edges of No-Arbitrage (http://ssrn.com/abstract=2664567) ]