Modelling financial volume curves with hierarchical Poisson processes

ArXiv ID: 2406.19402 “View on arXiv”

Authors: Unknown

Abstract

Modeling the trading volume curves of financial instruments throughout the day is of key interest in financial trading applications. Predictions of these so-called volume profiles guide trade execution strategies, for example, a common strategy is to trade a desired quantity across many orders in line with the expected volume curve throughout the day so as not to impact the price of the instrument. The volume curves (for each day) are naturally grouped by stock and can be further gathered into higher-level groupings, such as by industry. In order to model such admixtures of volume curves, we introduce a hierarchical Poisson process model for the intensity functions of admixtures of inhomogenous Poisson processes, which represent the trading times of the stock throughout the day. The model is based on the hierarchical Dirichlet process, and an efficient Markov Chain Monte Carlo (MCMC) algorithm is derived following the slice sampling framework for Bayesian nonparametric mixture models. We demonstrate the method on datasets of different stocks from the Trade and Quote repository maintained by Wharton Research Data Services, including the most liquid stock on the NASDAQ stock exchange, Apple, demonstrating the scalability of the approach.

Keywords: Volume Prediction, Poisson Process, Dirichlet Process, Market Microstructure, High-Frequency Trading

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper uses advanced hierarchical Bayesian nonparametrics (Dirichlet process mixtures, slice sampling MCMC) requiring significant mathematical sophistication, but also demonstrates practical application on real financial data (Wharton TAQ dataset) with scalable implementation details.

  flowchart TD
    A["Research Goal<br>Model intraday trading volume curves"] --> B{"Data Source<br>Trade and Quote repository<br>Wharton Research Data Services"}
    B --> C["Key Methodology<br>Hierarchical Poisson Process Model"]
    C --> D["Computational Process<br>Bayesian nonparametric mixture<br>via MCMC Slice Sampling"]
    D --> E["Key Finding 1<br>Scalability on liquid stocks<br>e.g., Apple"]
    D --> F["Key Finding 2<br>Effective for trade execution<br>strategies"]