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Asset Pricing with General Transaction Costs: Theory and Numerics

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  • Lukas Gonon
  • Johannes Muhle-Karbe
  • Xiaofei Shi

Abstract

We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their frictionless counterparts - the deviation has Ornstein-Uhlenbeck dynamics for quadratic costs whereas it follows a doubly-reflected Brownian motion if costs are proportional. More general models with arbitrary state dynamics and endogenous volatilities lead to multidimensional systems of nonlinear, fully-coupled forward-backward SDEs. These fall outside the scope of known wellposedness results, but can be solved numerically using the simulation-based deep-learning approach of Han, Jentzen and E (2018). In a calibration to time series of prices and trading volume, realistic liquidity premia are accompanied by a moderate increase in volatility. The effects of different cost specifications are rather similar, justifying the use of quadratic costs as a proxy for other less tractable specifications.

Suggested Citation

  • Lukas Gonon & Johannes Muhle-Karbe & Xiaofei Shi, 2019. "Asset Pricing with General Transaction Costs: Theory and Numerics," Papers 1905.05027, arXiv.org, revised Apr 2020.
    • Handle: RePEc:arx:papers:1905.05027
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    References listed on IDEAS

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    Cited by:

    1. Ashley Davey & Harry Zheng, 2020. "Deep Learning for Constrained Utility Maximisation," Papers 2008.11757, arXiv.org, revised Aug 2021.
    2. Isaenko, Sergey, 2023. "Transaction costs, frequent trading, and stock prices," Journal of Financial Markets, Elsevier, vol. 64(C).
    3. Johannes Muhle-Karbe & Xiaofei Shi & Chen Yang, 2020. "An Equilibrium Model for the Cross-Section of Liquidity Premia," Papers 2011.13625, arXiv.org.
    4. Ashley Davey & Harry Zheng, 2022. "Deep Learning for Constrained Utility Maximisation," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 661-692, June.
    5. Eunjung Noh & Kim Weston, 2020. "Price impact equilibrium with transaction costs and TWAP trading," Papers 2002.08286, arXiv.org.

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