Call–Put Implied-Volatility Spreads (CPIV)

Review package and reproduction code for a measurement note on call–put implied-volatility spreads (CPIV). The note maps paired European Black–Scholes–Merton (BSM) inversions exactly and tests how reliable the spread is under synthetic quote noise.

Definition

For a matched call–put pair (same underlying, strike, expiry, exercise style, and multiplier):

CPIV = 100 × (σ_C − σ_P)

The value is in percentage points, where σ_C and σ_P are the call and put implied volatilities.

Scope

• Every reported result is synthetic: European BSM inputs and simulated quote noise. The note uses no market quotes, option chains, returns, positions, or liquidation data.
• The note makes no alpha or trading claim.
• The repository also contains Hyperliquid collection and analysis code from a separate liquidation-exposure project. That code is outside the CPIV package and is not described here.

Contents

Path	Purpose
research/cpiv/manuscript_r11_proposed.md	Working manuscript (dated 18 October 2026)
research/cpiv/*.py	Diagnostics, audits, and benchmarks
research/cpiv/generated/	Generated CSV, JSON, SVG, and PNG evidence
dist/cpiv/quantcorner-cpiv-reviewed-2026-10-18-v28/	v28 (r26) review package: HTML, DOCX, PDF
reports/cpiv_v28_manifest_2026-10-18.sha256	SHA-256 manifest for the v28 package (268 entries)
reports/cpiv_v28_manifest_cpiv-only_2026-10-18.sha256	SHA-256 manifest for the CPIV-only subset (171 entries)
tests/test_cpiv_*.py	CPIV tests

Reproduce

Requires Python 3.12 or later and uv. CI runs the test suite on Ubuntu and Windows with Python 3.12, 3.13, and 3.14.

uv sync --locked --no-install-project
uv run python -m pytest tests -q

Regenerate the synthetic methods-note outputs into a fresh folder. The script refuses to write into a non-empty folder:

uv run python scripts/reproduce_cpiv_methods.py --output research/cpiv/generated/<fresh-name>

Verify the v28 package against its manifest:

pwsh -File scripts/verify_sha256_manifest.ps1 -ManifestPath reports/cpiv_v28_manifest_cpiv-only_2026-10-18.sha256 -RootPath .

The CPIV-only manifest checks the 171 CPIV files. The full manifest (reports/cpiv_v28_manifest_2026-10-18.sha256, 268 entries) also covers the non-CPIV v28 tree, which this repository does not contain in full, so it fails here by design.

The manifests do not cover README.md or CITATION.cff.

Limitations

• This is a measurement and methods note. It reports no empirical CPIV result.
• Simulated rankings and quote-noise results describe only the chosen synthetic generator and seeds.
• No independent replication by an outside party has been done.

Citing the CPIV review package (v28)

The CPIV review package (v28, r26, dated 18 October 2026) is archived on Zenodo:

• Version DOI: https://doi.org/10.5281/zenodo.23442601
• All versions (concept DOI): https://doi.org/10.5281/zenodo.23442600

Citation metadata is in CITATION.cff; the code is licensed under MIT (LICENSE).