Equilibrium under TWAP trading with quadratic transaction costs

TL;DR

This paper develops a continuous-time model to analyze how quadratic transaction costs influence equilibrium returns and stock holdings, using FBSDEs to characterize the solutions.

Contribution

It introduces a novel continuous-time risk-sharing model incorporating quadratic transaction costs and characterizes equilibrium via FBSDEs.

Findings

Equilibrium stock holdings are uniquely determined by FBSDEs.

Equilibrium returns are characterized as solutions to coupled linear FBSDEs.

The model provides insights into the impact of transaction costs on trading behavior.

Abstract

We study how transaction cost affects to the equilibrium return and optimal stock holdings in equilibrium. To this end, we develop a continuous-time risk-sharing model where heterogenous agents trade toward terminal target holdings subject to a quadratic transaction cost. The equilibrium stock holdings and trading rate under transaction cost are characterized by a unique solution to a forward-backward stochastic differential equation (FBSDE). The equilibrium return is also characterized as the unique solution of a system of coupled but linear FBSDEs.