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A Finite Difference Scheme for Pairs Trading with Transaction Costs

Author

Listed:
  • Zequn Li

    (Stevens Institute of Technology, 1 Castle Point on Hudson)

  • Agnès Tourin

    (New York University Tandon School of Engineering)

Abstract

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.

Suggested Citation

  • Zequn Li & Agnès Tourin, 2022. "A Finite Difference Scheme for Pairs Trading with Transaction Costs," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 601-632, August.
    • Handle: RePEc:kap:compec:v:60:y:2022:i:2:d:10.1007_s10614-021-10159-w
    DOI: 10.1007/s10614-021-10159-w
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