Trading Strategies within the Edges of No-Arbitrage

37 Pages Posted: 25 Sep 2015  

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Sebastian Jaimungal

University of Toronto - Department of Statistics

Jason Ricci

University of Toronto, Department of Statistics

Date Written: September 23, 2015

Abstract

We develop a trading strategy which employs limit and market orders in a multi-asset economy where the assets are not only correlated, but can also be structurally dependent. 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 provide a formal 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 midprices is from the no-arbitrage bounds. When midprices 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 midprice 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. Moreover, 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

JEL Classification: C6, C61, D81, G1, G13

Suggested Citation

Cartea, Álvaro and Jaimungal, Sebastian and Ricci, Jason, Trading Strategies within the Edges of No-Arbitrage (September 23, 2015). Available at SSRN: https://ssrn.com/abstract=2664567 or http://dx.doi.org/10.2139/ssrn.2664567

Álvaro Cartea (Contact Author)

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Sebastian Jaimungal

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://www.utstat.utoronto.ca/sjaimung

Jason Ricci

University of Toronto, Department of Statistics ( email )

Toronto, Ontario M5S 3G8
Canada

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