An Equilibrium Model for the Cross Section of Liquidity Premia

Abstract

We study a risk-sharing economy where an arbitrary number of heterogeneous agents trades an arbitrary number of risky assets subject to quadratic transaction costs. For linear state dynamics, the forward–backward stochastic differential equations characterizing equilibrium asset prices and trading strategies in this context reduce to a coupled system of matrix-valued Riccati equations. We prove the existence of a unique global solution and provide explicit asymptotic expansions that allow us to approximate the corresponding equilibrium for small transaction costs. These tractable approximation formulas make it feasible to calibrate the model to time series of prices and trading volume, and to study the cross section of liquidity premia earned by assets with higher and lower trading costs. This is illustrated by an empirical case study. Funding: J. Muhle-Karbe is partially supported by the CFM-Imperial Institute of Quantitative Finance. C. Yang is supported by the Hong Kong Research Grants Council [Grant 24207621] and a University Startup Grant from the Chinese University of Hong Kong.