{
  "title": "Forecasting Next-Settlement Funding from the Premium Integral: Mechanism-Based Ornstein–Uhlenbeck Evidence across Three Venues",
  "shortTitle": "Forecasting Next-Settlement Funding from the Premium Integral",
  "series": "humarb Research 06",
  "researchSeries": "humarb Research 06",
  "authors": [
    {
      "name": "Hang Liu",
      "orcid": "0009-0008-1059-3926",
      "orcidUrl": "https://orcid.org/0009-0008-1059-3926",
      "affiliation": "humarb Research, London, United Kingdom"
    }
  ],
  "url": "https://humarb.ai/research/",
  "paperPageUrl": "https://humarb.ai/research/premium-integral-funding/",
  "abstract": "Perpetual-futures funding is a deterministic transformation of a kernel-weighted premium integral, yet the integral is rarely used as the state variable in next-settlement forecasts. We derive exact discrete moments and clamped-normal predictive distributions under an Ornstein–Uhlenbeck premium model, then evaluate genuinely out-of-sample forecasts for BTC, ETH, and SOL on Binance, Gate, and Hyperliquid. The 38-day public-data sample contains 2,781 targets over 31 evaluation days. OU reduces pooled RMSE from 0.2368 bp for the last-settlement benchmark to 0.1968 bp, but remains slightly behind EWMA at 0.1947 bp. Improvements over Last are strongest on Hyperliquid; Binance and Gate favor EWMA over OU. Minute-level reconstruction supports linear rather than equal kernels on Binance and Gate. Twenty configurations and Holm/Reality-Check procedures address selection. Gaussian intervals fail by venue: 95% coverage is 39.1%, 43.5%, and 97.7%, respectively. The evidence supports mechanism-aware point forecasting, not uniformly superior accuracy, calibrated uncertainty, or executable net returns.",
  "keywords": [
    "perpetual futures",
    "funding rates",
    "premium integral",
    "Ornstein–Uhlenbeck process",
    "probabilistic forecasting",
    "forecast evaluation"
  ],
  "jel": [
    "G12",
    "G13",
    "G14",
    "C58"
  ],
  "language": "English",
  "resourceType": "Publication/Preprint",
  "type": "Methodological and empirical preprint",
  "version": "v1",
  "peerReviewed": false,
  "publisher": "Zenodo",
  "license": "CC-BY-4.0",
  "licenseUrl": "https://creativecommons.org/licenses/by/4.0/",
  "cites": [
    "10.5281/zenodo.23868361",
    "10.5281/zenodo.23897013"
  ],
  "doi": "10.5281/zenodo.23918114",
  "doiStatus": "Published",
  "versionDoi": "10.5281/zenodo.23918115",
  "versionDoiStatus": "Published",
  "zenodoRecordUrl": "https://zenodo.org/records/23918115",
  "zenodoRecordStatus": "Published",
  "publicationDate": "2026-11-03",
  "publicationDateStatus": "Published on Zenodo",
  "dataSnapshotDate": "2026-11-03",
  "samplePeriod": {
    "start": "2026-09-24T00:00:00Z",
    "endExclusive": "2026-11-01T00:00:00Z",
    "outOfSampleEvaluation": "2026-10-01 through 2026-10-31"
  },
  "pdf": "humarb-research-06-premium-integral-funding.pdf",
  "bibtex": "citation.bib",
  "chineseAbstract": "humarb-research-06-中文摘要.pdf",
  "reproductionPackage": "humarb-research-06-复现包.zip"
}