Paper: arXiv 2603.13170

Authors: Paul P. Hager, Ulrich Horst, Thomas Wagenhofer, Wei Xu

Abstract

We establish a microstructural foundation of the rough Bergomi model. Specifically, we consider a sequence of order driven financial market models where orders to buy or sell an asset arrive according to a Poisson process and have a long lasting impact on volatility. Using a recently established C-tightness result for càdlàg processes we establish the weak convergence of the price-volatility process to a log-normal rough volatility model. Our weak convergence result is accompanied by weak error rates that employ a recently established Clark-Ocone formula for Poisson processes and turn our microstructure model into viable alternative to classical simulation schemes. The weak error rates strongly hinge on Poisson arrival dynamics and are novel to the rough microstructure literature.

Complexity vs Empirical Score

  • Math Complexity: 9.2/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical proof linking order-driven microstructural market models to the rough Bergomi model via C-tightness and Clark-Ocone calculus for Poisson processes. While highly novel and mathematically sophisticated, it is purely theoretical with no empirical backtesting or real-market data application.

Research Flowchart

  flowchart TD
    A[Goal: Microstructural Foundation of Rough Bergomi Model] --> B[Input: Order-Driven Market Model<br>Poisson Order Arrivals & Long-Memory Volatility Impact]
    B --> C[Prove C-Tightness for Càdlàg Processes]
    C --> D[Establish Weak Convergence to Log-Normal Rough Volatility]
    D --> E[Derive Weak Error Rates via Poisson Clark-Ocone Formula]
    E --> F[Outcome: Microstructure Model as Viable Simulation Scheme]

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