Continuous-time Equilibrium Returns in Markets with Price Impact and Transaction Costs

ArXiv ID: 2405.14418 “View on arXiv”

Authors: Unknown

Abstract

We consider an Ito-financial market at which the risky assets’ returns are derived endogenously through a market-clearing condition amongst heterogeneous risk-averse investors with quadratic preferences and random endowments. Investors act strategically by taking into account the impact that their orders have on the assets’ drift. A frictionless market and an one with quadratic transaction costs are analysed and compared. In the former, we derive the unique Nash equilibrium at which investors’ demand processes reveal different hedging needs than their true ones, resulting in a deviation of the Nash equilibrium from its competitive counterpart. Under price impact and transaction costs, we characterize the Nash equilibrium as the (unique) solution of a system of FBSDEs and derive its closed-form expression. We furthermore show that under common risk aversion and absence of noise traders, transaction costs do not change the equilibrium returns. On the contrary, when noise traders are present, the effect of transaction costs on equilibrium returns is amplified due to price impact.

Keywords: Nash equilibrium, FBSDEs, quadratic transaction costs, price impact, strategic investors, Equities (Risky Assets)

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is heavily mathematical, employing stochastic calculus, Itô processes, FBSDEs, and Nash equilibrium analysis, which scores high on math complexity. However, it presents a purely theoretical model with no backtesting, data analysis, or implementation details, placing it in the Lab Rats quadrant.

  flowchart TD
    A["Research Goal<br>Determine equilibrium returns with price impact & transaction costs"] --> B["Model Setup<br>Continuous-time Ito market"]
    B --> C{"Model Configuration"}
    C --> C1["Frictionless Market"]
    C --> C2["Quadratic Transaction Costs"]
    C1 --> D["Solve Nash Equilibrium<br>FBSDEs / Strategic Pricing"]
    C2 --> D
    D --> E["Key Outcomes"]
    E --> E1["Frictionless: Investors' demand differs from true hedging needs<br>Nash ≠ Competitive equilibrium"]
    E --> E2["Costs & Impact: Closed-form solution derived<br>Costs amplify returns via price impact when noise traders exist"]
    E --> E3["No Noise Traders: Transaction costs do not alter equilibrium returns"]