Asset pricing with general transaction costs: Theory and numerics

Gonon, Lukas ; Muhle-Karbe, Johannes and Shi, Xiaofei (2021): Asset pricing with general transaction costs: Theory and numerics. In: Mathematical Finance, Vol. 31, No. 2: pp. 595-648

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 well-posedness 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0960-1627
• Language: English