Pith Number

pith:J3PJRCTO

pith:2026:J3PJRCTOCM3G4HXYYCXZ34NDLI

not attested not anchored not stored refs resolved

Robust Volatility Index Calculation with OTM Option-implied Probability

Masaaki Fukasawa, Shunta Murayama

A construction turns discrete OTM bid-ask spreads into a continuous arbitrage-free option pricing function using fewer parameters than prior methods.

arxiv:2605.17446 v1 · 2026-05-17 · q-fin.MF

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4 Citations open

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Claims

C1strongest claim

The proposed construction produces a continuous European option pricing function consistent with observed OTM bid-ask spreads, strictly satisfying arbitrage-free conditions such as monotonicity and convexity, while requiring fewer market parameters than existing methods and thereby enabling robust volatility index calculation even in extremely low-liquidity markets.

C2weakest assumption

That a continuous arbitrage-free pricing function can be constructed from discrete OTM bid-ask data using strictly fewer parameters than prior methods while remaining consistent with all observed spreads and satisfying the required shape constraints without introducing new fitting instabilities.

C3one line summary

A construction of continuous European option prices from OTM bid-ask data with fewer parameters enables robust model-free volatility index calculation under no-arbitrage.

References

9 extracted · 9 resolved · 0 Pith anchors

[1] arXiv preprint arXiv:2601.11209 , year= 2026

[2] Carr, P . and Madan, D. (2001). Towards a Theory of Volatility Trading. Handbooks in Mathematical Finance: Option Pricing, Interest Rates and Risk Management. Cambridge University Press. 458-476 2001

[3] Cboe Exchange, Inc. (2022). Cboe Volatility Index Mathematics Methodol- ogy. Cboe Global Markets 2022

[4] Cboe Global Indices, LLC. (2024). Volatility Index Methodology: Cboe Volatility Index. Cboe Global Markets 2024

[5] and Ya- mazaki, K 2011 · doi:10.1142/s0219024911006681

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:39.339700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ede988a6e13366e1ef8c0af9df1a35a137983c71bdf6d42dd2d2ccc50a61b2d

Aliases

arxiv: 2605.17446 · arxiv_version: 2605.17446v1 · doi: 10.48550/arxiv.2605.17446 · pith_short_12: J3PJRCTOCM3G · pith_short_16: J3PJRCTOCM3G4HXY · pith_short_8: J3PJRCTO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/J3PJRCTOCM3G4HXYYCXZ34NDLI \
  | 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: 4ede988a6e13366e1ef8c0af9df1a35a137983c71bdf6d42dd2d2ccc50a61b2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e870d176d8eb3235585328453d3cad3060767bf7c93307aff84b7a8f46b0172e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-fin.MF",
    "submitted_at": "2026-05-17T13:36:53Z",
    "title_canon_sha256": "7314b791ed2c8e8a36983a96de3c9f97149d1abbd87bbbce8a551e29573b524a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17446",
    "kind": "arxiv",
    "version": 1
  }
}