The Microdiffusion: Book-State Price Risk and Heavy Tails in Event Time

Anonymized replication package for:

The Microdiffusion: Book-State Price Risk and Heavy Tails in Event Time (author identities withheld for double-anonymized peer review)

What the paper shows

In event time, the one-step conditional variance of the log mid-price is a function of the visible book state, the diffusion surface a_xx(I, S) over best-level imbalance I and relative spread S. The innovation that remains after scaling by that surface is heavy-tailed and is well described by a Generalized Hyperbolic law. A nested forecast comparison then asks which part of the state carries out-of-sample predictive value: the quoted spread carries the transferable one-step forecast content (it predicts both whether the mid moves and how large the move is), while the imbalance is a real contemporaneous second-moment modulation that adds no one-step point-forecast increment and does not transfer as a day-to-day shape.

Core hypotheses and results

The paper rests on one maintained assumption (H1) and four substantive hypotheses (H2-H5):

• H1 (maintained): the conditional drift is effectively two-dimensional in the book state (I, S); the price level adds no further information about the expected next move, and is the coordinate left free to diffuse.
• H2: the microdiffusion a_xx(I, S) is a stable function of the book state, reappearing on disjoint, unseen days.
• H3: a Gaussian innovation is insufficient; the scaled residual is heavy-tailed and requires a Generalized Hyperbolic law.
• H4: scale (the surface) and shape (the heavy tail) are separately identified and each is necessary.
• H5: the one-step forecast content of the state is concentrated in the spread; the imbalance moves the contemporaneous variance but adds no further one-step accuracy.

Headline results: the state-to-variance ranking transfers out of sample, the spread-driven level transfers across days, instruments, and volatility regimes, the imbalance transfers weakly as a shape; the heavy-tailed innovation reduces extreme-tail under-coverage in intraday VaR backtests and ties a jointly estimated GARCH-t on predictive log score while beating its Gaussian version.

Repository layout

microdiffusion/
  src/
    common/      shared configuration, figure style, and portable paths
    data/        event-panel assembly from the processed L1 files
    engine/      the model object: diffusion surface and GH innovation law
    analysis/    the tests and decompositions that produce the results
    figures/     manuscript figure and table scripts
  results/       article tables written by the analyses (with digests.sha256)
  data/          raw and processed inputs, git-ignored (see data/README.md)
  reproduce.py   single deterministic entry point with digest checks
  requirements.txt
  .env.example

The src/ subpackages are split by role, not by chapter. Every path resolves relative to the repository root through src/common/paths.py; nothing depends on the current working directory or a machine-specific path.

Requirements

python -m venv .venv && source .venv/bin/activate
pip install -r requirements.txt

Python 3.11. No credentials are needed; see .env.example.

Reproduce

python reproduce.py            # full chain, then verify every tracked digest
python reproduce.py --fast     # event panel + gated tables + verify
python reproduce.py --check    # verify digests of existing results only

reproduce.py runs the stages in dependency order (data, engine, analysis, figures) and checks each tracked result in results/ against results/digests.sha256. The digest-gated outputs are the forecast tables plus the pooled descriptive table descriptive_stats_qse.csv; these are exactly what --fast regenerates before verifying. The remaining engine, robustness, benchmark and figure stages are run for completeness and write diagnostic tables and manuscript figures that are not tracked.

Note the difference between the modes: --check only re-hashes the tracked results/*.csv already on disk against the manifest (a fast integrity check, it recomputes nothing), whereas --fast and the full run regenerate the gated tables from the data and then verify. A genuine reproduction therefore requires a --fast or full run, not --check alone.

Data

See data/README.md. The processed L1 parquet files are available to referees and replicators on request through the journal's editorial system (author contact withheld for double-anonymized review). Raw exchange data is proprietary and cannot be redistributed.