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Derivatives Pricer – Implied Volatility Surface
x402
Derivatives Pricer – Implied Volatility Surface is a paid API for AI agents from derivatives-pricer-production.up.railway.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-10-11).
Computes a full implied volatility surface from a grid of market option quotes using Black-Scholes inversion, returning per-point IVs, Greeks, fit statistics, and a structured vol surface matrix.
Price / call$0.1
Success—
StatusUnknown
How this service works
x402-paid Black-Scholes European option pricing, Greeks, IV surfaces, price/scenario on submitted smiles (TV bilinear), portfolio risk, free demo, and MCP. USDC exact on Solana (PayAI) and/or Base (CDP when configured). Receive wallets appear only in HTTP 402, never on free discovery.
Output
Returns a structured JSON with: a 'surface' object containing a strikes array, maturities array, and 2D impliedVols grid; a 'points' array with per-option results (implied vol, model price, price error, status, and full analytic Greeks: delta, gamma, vega, theta, rho); a 'fit' object with RMSE, max absolute error, mean absolute error, ok/failed counts; 'stats' with solver info and elapsed time; 'market' echoing rate and dividend yield; and a requestId/computedAt timestamp.
Example use cases
Equity options vol smile calibration
“I have a set of SPY call and put quotes across 3 strikes (490, 500, 510) and 2 maturities (3 months and 6 months) with the underlying at 502, a 5% risk-free rate, and a 1.5% dividend yield. Can you invert Black-Scholes on all of them and give me the implied vol surface, per-point Greeks, and RMSE fit quality?”
FX options tenor surface construction
“Build an implied vol surface for EUR/USD options: spot at 1.08, strikes 1.05, 1.08, and 1.11, maturities 0.25, 0.5, and 1 year, risk-free rate 4.5%, foreign rate 3.5% as dividend yield. I have observed call premiums of 0.032, 0.018, and 0.009 — return the IV grid and deltas.”
Commodity options vol grid for risk desk
“I've got a book of natural gas European call options with different forward levels per maturity — underlying 2.80 for the 3-month, 2.95 for the 6-month, strikes ranging from 2.50 to 3.20, risk-free rate 5%, convenience yield 2%. Fit implied vols to all the observed market premiums and give me the full vol surface plus vega and theta for each point.”
Technical details
Endpoint
POSThttps://derivatives-pricer-production.up.railway.app/v1/volatility/surface?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need a complete implied volatility surface calibrated from market quotes across multiple strikes and maturities in a single call, rather than inverting one option at a time. It is ideal when you want fit diagnostics (RMSE, per-point errors), per-point Greeks alongside IVs, and a structured vol grid ready for downstream risk or pricing use. Prefer this over single-IV endpoints when building smile/skew visualizations, calibrating term structure, or aggregating risk across a multi-leg options book.
Side effects
- Option with non-positive underlying or strike returns validation error
- Premium below intrinsic value causes IV solver failure (status: 'failed' on that point)
- Duplicate (underlying, strike, maturity, type) keys are averaged silently
- More than 200 options in one request rejected (maxItems constraint)
- Payment failure (x402 USDC transaction rejected or insufficient balance) blocks the call
- Deep in-the-money or zero-time options may fail convergence and appear as null in the surface grid
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| rate | number | Shared continuous risk-free / discount rate r for the book (e.g. 0.05 = 5%). |
| options | array | Market quotes: one object per (underlying, strike, maturity, type) with observed premium. Prefer unique keys per cell; duplicates average into the grid. |
| treeSteps | integer | CRR steps when optionStyle is american. |
| expiration | string | Shared ISO-8601 window end for all rows. When set, all rows share derived τ. |
| optionStyle | string | Exercise style for IV solve (default "european"). |
| forwardStart | string | Shared ISO-8601 window start for all rows (optional). |
| dividendYield | number | Shared continuous yield q (default 0): equity dividends, FX foreign rate, or commodity convenience yield as appropriate. |
Output
Schema · Response
{
"type": "json",
"example": {
"fit": {
"okCount": 3,
"failedCount": 0,
"rmsePriceError": 1.2e-8,
"maxAbsPriceError": 2e-8,
"meanAbsPriceError": 1e-8
},
"stats": {
"solver": "fastImpliedVol",
"elapsedMs": 1.2,
"optionCount": 3,
"avgIterations": 4
},
"market": {
"rate": 0.05,
"dividendYield": 0
},
"points": [
{
"index": 0,
"greeks": {
"rho": 10,
"vega": 15,
"delta": 0.75,
"gamma": 0.02,
"theta": -8
},
"status": "ok",
"strike": 90,
"premium": 12.5,
"impliedVol": 0.25,
"modelPrice": 12.5,
"optionType": "call",
"priceError": 0,
"underlying": 100,
"timeToExpiry": 0.25
}
],
"surface": {
"strikes": [
90,
100,
110
],
"maturities": [
0.25,
0.5,
1
],
"impliedVols": [
[
0.25,
null,
null
],
[
null,
0.22,
null
],
[
null,
null,
0.2
]
]
},
"requestId": "00000000-0000-4000-8000-000000000002",
"computedAt": "2026-01-01T00:00:00.000Z"
}
}Tags
x402
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