A Monotone Finite Difference Scheme for Pairs Trading with Transaction Costs
We consider a pairs trading stochastic control problem with transaction costs and constraints on the gross market exposure, and propose a new monotone Finite Difference scheme approximating the viscosity solution of the Hamilton-Jacobi-Bellman equation characterizing the optimal trading strategies. Given a fixed time horizon and a portfolio of two cointegrated assets, the agent trades the spread between the two assets and the trading strategy is defined as the possibly negative portfolio weight maximizing the expected exponential utility derived from terminal wealth. Furthermore, trades incur transaction costs comprised of explicit transactions fees and commissions and the implicit cost due to slippage. These costs are modeled as a linear or square root function of the trading rate and respectively added or subtracted from the observable asset price at the time when a buy or a sell order enters the market. Our main contribution is the derivation of a robust approximation for the nonlinear transaction cost term in the Hamilton-Jacobi-Bellman equation. Finally, we combine our monotone Finite Difference scheme with a Monte Carlo sampling method to analyze the effects of transaction fees and slippage on the trading policies' performance.
Agnes Tourin grew up in the suburbs of Paris and graduated from the Grande Ecole Mines Paris-PSL. In 1992, she received a Ph.D. in applied mathematics from University Paris-Dauphine.Subsequently, she held a tenured position in Paris, followed by several positions in Canada: a limited term position at University of Toronto, a tenure-track position at McMaster University, in Hamilton, Ontario, and a part-time visiting position at the Fields Institute. In 2005, she moved to New York and stayed at home to care for her two children for 5 years. Since 2010, she has been teaching financial engineering to master’s students at NYU Tandon and is currently the Finance and Risk Engineering Department Interim Chair. She is also a Senator on the Full-time Continuing Contract Faculty Senators Council (C-FSC), a member of the C-FSC committee on Diversity, Equity and Inclusion, and on the Tandon Faculty Executive Committee. She also recently served on the NYU President search committee.