Optimal execution and speculation with trade signals

ArXiv ID: 2306.00621 “View on arXiv”

Authors: Unknown

Abstract

We propose a price impact model where changes in prices are purely driven by the order flow in the market. The stochastic price impact of market orders and the arrival rates of limit and market orders are functions of the market liquidity process which reflects the balance of the demand and supply of liquidity. Limit and market orders mutually excite each other so that liquidity is mean reverting. We use the theory of Meyer-$σ$-fields to introduce a short-term signal process from which a trader learns about imminent changes in order flow. Her trades impact the market through the same mechanism as other orders. With a novel version of Marcus-type SDEs we efficiently describe the intricate timing of market dynamics at moments when her orders concur with that of others. In this setting, we examine an optimal execution problem and derive the Hamilton–Jacobi–Bellman (HJB) equation for the value function of the trader. The HJB equation is solved numerically and we illustrate how the trader uses the signals to enhance the performance of execution problems and to execute speculative strategies.

Keywords: Price Impact Models, Optimal Execution, Market Microstructure, HJB Equation, Stochastic Calculus

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats
  • Why: The paper is highly mathematical, featuring advanced stochastic calculus (Meyer-σ-fields, Marcus SDEs) and a complex HJB-QVI, but lacks empirical validation, relying solely on illustrative simulations without real-world data or performance metrics.
  flowchart TD
    A["Research Goal: Model optimal execution & speculation with trade signals"] --> B["Methodology: Stochastic price impact model with liquidity process"]
    B --> C["Inputs: Market order flow, liquidity dynamics, short-term signals"]
    C --> D["Computation: Formulate HJB equation via Marcus-type SDEs"]
    D --> E["Numerical solution of HJB for optimal policy"]
    E --> F["Outcomes: Enhanced execution performance & viable speculative strategies"]