Paper: arXiv 2310.09273

Abstract

The primary objective of this paper is to conceive and develop a new methodology to detect notable changes in liquidity within an order-driven market. We study a market liquidity model which allows us to dynamically quantify the level of liquidity of a traded asset using its limit order book data. The proposed metric holds potential for enhancing the aggressiveness of optimal execution algorithms, minimizing market impact and transaction costs, and serving as a reliable indicator of market liquidity for market makers. As part of our approach, we employ Marked Hawkes processes to model trades-through which constitute our liquidity proxy. Subsequently, our focus lies in accurately identifying the moment when a significant increase or decrease in its intensity takes place. We consider the minimax quickest detection problem of unobservable changes in the intensity of a doubly-stochastic Poisson process. The goal is to develop a stopping rule that minimizes the robust Lorden criterion, measured in terms of the number of events until detection, for both worst-case delay and false alarm constraint. We prove our procedure’s optimality in the case of a Cox process with simultaneous jumps, while considering a finite time horizon. Finally, this novel approach is empirically validated by means of real market data analyses.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematics including Marked Hawkes processes, minimax quickest detection theory, and proofs of optimality for Cox processes with simultaneous jumps, earning a high math score. While it validates the approach with real market data and provides statistical goodness-of-fit, the empirical section appears less exhaustive than a full backtest implementation, warranting a moderate empirical rigor score.

Research Flowchart

  flowchart TD
  A["Research Goal: Detect liquidity changes in order-driven markets"] --> B["Data Input: Limit Order Book Data"]
  B --> C["Methodology: Marked Hawkes Processes"]
  C --> D["Proxy: Trades-through as liquidity metric"]
  D --> E["Computational Process: Minimax Quickest Detection"]
  E --> F["Optimization: Minimize Lorden Criterion"]
  F --> G["Key Outcomes: Optimal stopping rule for intensity changes"]
  G --> H["Empirical Validation: Real market data analysis"]