Paper: arXiv 2604.23608

Authors: Chris Angstmann, Tim Gebbie

Abstract

Financial markets are often modelled as if time were unique and continuous across assets and markets. Financial markets are however asynchronous, order flow is event-driven, and waiting times between events are often random. Many of the most influential formulations of financial market models presuppose a unique global calendar time and advocate for this or that preferred single latent continuous-time price system. Here we critically contrast these assumptions with event-time, renewal, point-process, and order-flow descriptions. We revisit no-arbitrage, no-dynamic-arbitrage, and risk-neutral option pricing in settings where the market is represented as a discrete event system and where the continuum limit of a discrete-time random walk need not be unique. The central suggestion is then that such non-uniqueness points to a more foundational form of market incompleteness than is usually emphasized. This highlights the importance of operational time at the level of decision making but reminds market practitioners that managing risk itself often requires reconciling operational time with a global calendar time. At these longer time scales forms of effective or average completeness may still emerge at lower frequencies and remain useful for portfolio construction and risk management, even if high-frequency hedging and execution expose a clock mismatch between trading, pricing, and longer-horizon allocation.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper focuses on the theoretical and ontological foundations of time, price representation, and market incompleteness using stochastic processes, point-process theory, and differential limits. While it references technical frameworks, it does not provide an implementation, backtest, or a novel quantitative empirical study.

Research Flowchart

  flowchart TD
    A[<b>Goal:</b> Analyze market impacts of non-unique time vs. global calendar time] --> B[<b>Inputs:</b> Order flow data, Event-time datasets, Point-process models]
    B --> C{<b>Methodology:</b> Contrast continuous-time models with discrete event-systems}
    C --> D[<b>Computation:</b> Test no-arbitrage & risk-neutral pricing under random wait times]
    D --> E[<b>Outcomes:</b> Non-uniqueness reflects foundational market incompleteness]
    E --> F[<b>Conclusion:</b> Reconciling operational vs. calendar time for risk management]

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0 of 53 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.