Asset Pricing with General Transaction Costs: Theory and Numerics

45 Pages Posted: 3 Jun 2019 Last revised: 16 Apr 2020

See all articles by Lukas Gonon

Lukas Gonon

Ludwig-Maximilians-Universität München

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics

Xiaofei Shi

Carnegie Mellon University - Department of Mathematical Sciences

Date Written: April 15, 2020

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.

Keywords: Radner equilibrium, transaction costs, forward-backward SDEs, deep learning

JEL Classification: C68, D52, G11, G12

Suggested Citation

Gonon, Lukas and Muhle-Karbe, Johannes and Shi, Xiaofei, Asset Pricing with General Transaction Costs: Theory and Numerics (April 15, 2020). Available at SSRN: https://ssrn.com/abstract=3387232 or http://dx.doi.org/10.2139/ssrn.3387232

Lukas Gonon

Ludwig-Maximilians-Universität München ( email )

Johannes Muhle-Karbe (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Xiaofei Shi

Carnegie Mellon University - Department of Mathematical Sciences ( email )

Pittsburgh, PA 15213-3890
United States

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