Equilibrium Asset Pricing with Quadratic Trading Costs

Summary

This paper studies equilibrium prices and trading strategies in risk-sharing economies where heterogeneous agents face quadratic transaction costs. It characterizes the equilibrium with a coupled system of forward-backward stochastic equations, which jointly describes the evolution of economic states and agents' decisions. The authors establish that a unique solution generally exists when agents' preferences are sufficiently similar.

In a benchmark with linear state dynamics, the model links transaction costs and volatility to observed illiquidity discounts and liquidity premia: higher costs correspond to a positive relationship with volatility. The result offers a theoretical way to interpret how trading frictions can shape asset prices. The document provides no numerical calibration, empirical dataset, or trading-performance test, and its existence result depends on the stated preference condition, limiting direct conclusions about how well the framework fits particular markets.

Key ideas

• The model examines equilibrium prices and strategies when agents bear quadratic trading costs.
• Equilibrium is characterized by a coupled forward-backward stochastic system.
• A unique solution generally exists when agents' preferences are sufficiently similar.
• In a linear-dynamics benchmark, transaction costs and volatility are positively related to illiquidity discounts and liquidity premia.
• The document presents a theoretical result without empirical calibration or strategy evaluation.

Tags

# Equilibrium Asset Pricing with Transaction Costs


# Equilibrium Asset Pricing with Transaction Costs









We study risk-sharing economies where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled forward-backward stochastic differential equations. We show that a unique solution generally exists provided that the agents' preferences are sufficiently similar. In a benchmark specification with linear state dynamics, the illiquidity discounts and liquidity premia observed empirically correspond to a positive relationship between transaction costs and volatility.

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