Paper: arXiv 2407.17401

Abstract

Starting from a basic model in which the dynamic of the transaction prices is a geometric Brownian motion disrupted by a microstructure white noise, corresponding to the random alternation of bids and asks, we propose moment-based estimators along with their statistical properties. We then make the model more realistic by considering serial dependence: we assume a geometric fractional Brownian motion for the price, then an Ornstein-Uhlenbeck process for the microstructure noise. In these two cases of serial dependence, we propose again consistent and asymptotically normal estimators. All our estimators are compared on simulated data with existing approaches, such as Roll, Corwin-Schultz, Abdi-Ranaldo, or Ardia-Guidotti-Kroencke estimators.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents advanced stochastic processes (fractional Brownian motion, Ornstein-Uhlenbeck) and moment-based derivations with asymptotic normality proofs, scoring high in math; it rigorously tests estimators on both simulated and real data, comparing against established benchmarks, indicating strong empirical rigor.

Research Flowchart

  flowchart TD
  G["Research Goal: Develop estimators for<br/>bid-ask spreads incorporating serial dependence<br/>(Fractional Brownian Motion & Ornstein-Uhlenbeck)"] --> M["Methodology: Moment-Based Estimation"]
  M --> D["Data: Simulated Financial Data<br/>(GBM, fBM, OU processes)"]
  D --> C["Computation: Deriving & evaluating<br/>statistical properties (Consistency, Asymptotic Normality)"]
  C --> E["Evaluation: Comparison with benchmarks<br/>(Roll, Corwin-Schultz, Abdi-Ranaldo, Ardia-Guidotti-Kroencke)"]
  E --> F["Findings: New consistent estimators for<br/>serially dependent models validated via simulation"]