TRADING STRATEGIES WITHIN THE EDGES OF NO-ARBITRAGE

Álvaro Cartea, Sebastian Jaimungal () and Jason Ricci ()
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Álvaro Cartea: Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
Sebastian Jaimungal: #x2020;Department of Statistical Sciences, University of Toronto, Toronto, ON, Canada M5T 1P5, Canada
Jason Ricci: #x2020;Department of Statistical Sciences, University of Toronto, Toronto, ON, Canada M5T 1P5, Canada

International Journal of Theoretical and Applied Finance (IJTAF), 2018, vol. 21, issue 03, 1-37

Abstract: We develop a trading strategy that employs limit and market orders in a multiasset economy where the assets are not only correlated, but can also be structurally dependent. To model the structural dependence, the mid-price processes follow a multivariate reflected Brownian motion on the closure of a no-arbitrage region which is dictated by the bid–ask spreads of the assets. We provide a mathematical framework for such an economy and solve for the value function and optimal control for an investor who takes positions in these assets. The optimal strategy exhibits two dominant features which depend on how far the vector of mid-prices is from the no-arbitrage bounds. When mid-prices are sufficiently far from the no-arbitrage edges, the strategy behaves as that of a market maker who posts buy and sell limit orders. And when the mid-price vector is close to the edge of the no-arbitrage region, the strategy executes a combination of market orders and limit orders to profit from statistical arbitrages. We discuss a numerical scheme to solve for the value function and optimal control, and perform a simulation study to discuss the main characteristics of the optimal strategy.

Keywords: Optimal trading; high-frequency trading; algorithmic trading; limit orders; market orders; stochastic control; impulse control; no-arbitrage bounds (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0219024918500255

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