Pith Number

pith:M7ZM724C

pith:2026:M7ZM724CKQ2U42G4Q36SAW6LNB

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Differential Machine Learning for 0DTE Options with Stochastic Volatility and Jumps

Takayuki Sakuma

A three-stage differential machine learning procedure approximates jump terms more accurately in ultra-short maturity options while preserving pricing accuracy and delivering faster Greeks than Fourier methods.

arxiv:2603.07600 v4 · 2026-03-08 · q-fin.CP

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Claims

C1strongest claim

The method improves jump-term approximation relative to one-stage baselines while maintaining comparable pricing errors. Furthermore, it reduces errors in Greeks, produces stable one-day delta hedges, and offers significant speedups over Fourier-based benchmarks.

C2weakest assumption

That the three-stage joint training of pricing and jump-operator networks, together with the maturity-gated variance correction, reliably identifies jump terms and produces accurate Greeks for ultra-short maturities without overfitting to the specific training data or model assumptions.

C3one line summary

A three-stage differential ML method prices 0DTE options under SVJD by combining Black-Scholes with maturity-gated variance correction, joint pricing and jump-operator networks, and PIDE-residual penalties to improve jump approximation and Greeks while speeding up computation.

Receipt and verification

First computed	2026-06-09T02:07:23.351847Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67f2cfeb8254354e68dc86fd205bcb6851ff5832fec39cc7e0aa33e16a753127

Aliases

arxiv: 2603.07600 · arxiv_version: 2603.07600v4 · doi: 10.48550/arxiv.2603.07600 · pith_short_12: M7ZM724CKQ2U · pith_short_16: M7ZM724CKQ2U42G4 · pith_short_8: M7ZM724C

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/M7ZM724CKQ2U42G4Q36SAW6LNB \
  | 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: 67f2cfeb8254354e68dc86fd205bcb6851ff5832fec39cc7e0aa33e16a753127

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d82d2e74083e135083ed3672a40da590a481fb8deca130cc5ff40e29bc54fd8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-fin.CP",
    "submitted_at": "2026-03-08T12:10:24Z",
    "title_canon_sha256": "9a9040508f4b80e7a6d6fd4777c881eab81d45e3a0b132ecd32343f8c2754abb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.07600",
    "kind": "arxiv",
    "version": 4
  }
}