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Derivatives Pricer — Implied Volatility (Single Premium)
x402
Derivatives Pricer — Implied Volatility (Single Premium) is a paid API for AI agents from derivatives-pricer-production.up.railway.app, paid per call via x402, $0.03/call, status unknown (last checked 2026-10-11).
Computes implied volatility from an observed option premium using Black-Scholes, returning IV, converged model price, price error, and full analytic Greeks.
Price / call$0.03
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 JSON object with the computed implied volatility (as a decimal, e.g. 0.20 = 20%), whether the Newton-Raphson solver converged, the number of iterations taken, the Black-Scholes model price at that IV, the price error versus the input premium, the five analytic Greeks (delta, gamma, theta, vega, rho), a mirror of the original inputs, a requestId, and a timestamp.
Example use cases
Trader verifying IV on live quote
“I'm looking at a European put on a stock trading at 98, strike 100, market premium is 5.20, expiring in 3 months, risk-free rate 4.5%, no dividends — what implied volatility does that premium imply, and what are the Greeks?”
Quant model calibration check
“I need to back out the implied vol from a European call: underlying 200, strike 210, observed premium 12.75, time to expiry 0.25 years, rate 5%, dividend yield 1.5%. Does the model converge and what's the implied vol?”
Options educator building example
“For a textbook example, solve for the implied volatility of an at-the-money European call where underlying equals strike at 100, market premium is 10.45, one year to expiry, 5% risk-free rate, and zero dividends — and show me all the Greeks too.”
Technical details
Endpoint
POSThttps://derivatives-pricer-production.up.railway.app/v1/option/implied-vol?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need to invert an observed market premium to its implied volatility under Black-Scholes for a European option, especially when you also need analytic Greeks in the same call. Prefer it over a full options chain or surface endpoint when you have a single premium observation. Because it requires no API keys and charges a flat $0.03 USDC per call via x402, it is ideal for agent workflows needing on-demand, pay-per-use IV computation without credential management.
Side effects
- Non-convergence: if the premium is outside the no-arbitrage bounds or the solver cannot converge within its iteration limit, 'converged' will be false and impliedVol may be null or unreliable
- Invalid inputs: strike or underlying <= 0 returns a 400-level validation error
- Negative premium or premium exceeding intrinsic value causes solver divergence
- Very short or zero timeToExpiry can cause numerical instability in vega and thus IV solver failure
- Payment failure: if the x402 USDC micropayment on Solana or Base is not completed, the request is rejected with a 402 Payment Required
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| rate | number | Continuous risk-free rate r |
| strike | number | Strike K (> 0) |
| premium | number | Observed market premium |
| treeSteps | integer | |
| expiration | string | |
| optionType | string | |
| underlying | number | Underlying price S (> 0) |
| optionStyle | string | |
| forwardStart | string | |
| timeToExpiry | number | Time to expiry in years (xor expiration) |
| dividendYield | number | Continuous yield q (default 0) |
Output
Schema · Response
{
"type": "json",
"example": {
"model": "black-scholes-merton",
"greeks": {
"rho": 53.23248343,
"vega": 37.52403469,
"delta": 0.63683059,
"gamma": 0.01876202,
"theta": -6.41402764
},
"inputs": {
"rate": 0.05,
"strike": 100,
"premium": 10.45057562,
"optionType": "call",
"underlying": 100,
"optionStyle": "european",
"timeToExpiry": 1,
"dividendYield": 0
},
"converged": true,
"requestId": "00000000-0000-4000-8000-000000000003",
"computedAt": "2026-01-01T00:00:00.000Z",
"impliedVol": 0.2,
"iterations": 12,
"modelPrice": 10.45057562,
"priceError": 0,
"optionStyle": "european",
"greeksQuality": "analytic"
}
}Tags
x402
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