Pith Number

pith:JPIUXA2C

pith:2026:JPIUXA2CRRGRE6FHGY7MMYVSGY

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A Hybrid Gaussian Process Regression Framework for Stable Volatility-Covariance Estimation: Evidence from Global Equity Indices

Ujjwala Vadrevu

A hybrid framework models individual equity volatilities with Gaussian process regression while using historical data for correlations to produce stable and regulatory-compliant VaR and ES estimates.

arxiv:2605.17275 v1 · 2026-05-17 · q-fin.RM · cs.LG

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\pithnumber{JPIUXA2CRRGRE6FHGY7MMYVSGY}

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Claims

C1strongest claim

the GPR-HS framework achieves regulatory compliance in the majority of test splits; including a 100% ES pass rate at the portfolio level, while outperforming the static Historical VaR benchmark in 71.4% of univariate cases by Quadratic Loss and 100% of cases by violation count.

C2weakest assumption

The assumption that inter-asset correlations estimated from historical covariance remain sufficiently stable and representative during the forward-chaining test periods (June 2020-June 2025), such that the hybrid decoupling does not introduce systematic bias in portfolio-level VaR/ES forecasts.

C3one line summary

A hybrid GPR-HS framework models volatilities via univariate Gaussian processes with Matern 5/2 kernel and correlations via historical covariance, with Aggressive Noise Initialization for stability, achieving high regulatory compliance on seven global equity indices over 2020-2025.

References

2 extracted · 2 resolved · 0 Pith anchors

[1] Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, 2002 · doi:10.2307/1912773

[2] Market Risk Assessment of a trading book using Statistical and Machine Learning 2015 · doi:10.1016/s0927-5398(00)00012-8

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:49.238756Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bd14b83428c4d1278a7363ec662b23634b921d0c74529f09de9577702d7c76e

Aliases

arxiv: 2605.17275 · arxiv_version: 2605.17275v1 · doi: 10.48550/arxiv.2605.17275 · pith_short_12: JPIUXA2CRRGR · pith_short_16: JPIUXA2CRRGRE6FH · pith_short_8: JPIUXA2C

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JPIUXA2CRRGRE6FHGY7MMYVSGY \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 4bd14b83428c4d1278a7363ec662b23634b921d0c74529f09de9577702d7c76e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a17e539a622641463ac67df7faf9ee7038ebb2708871a2becb77a8569178cc67",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "q-fin.RM",
    "submitted_at": "2026-05-17T05:52:54Z",
    "title_canon_sha256": "1b1f922348c989f28807c849c7a78f07a1818bdaf2a5f39e045c0d85ced99cc5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17275",
    "kind": "arxiv",
    "version": 1
  }
}