Derivatives Pricer – Black-Scholes European Option Pricing

x402

Derivatives Pricer – Black-Scholes European Option Pricing is a paid API for AI agents from derivatives-pricer-production.up.railway.app, paid per call via x402, $0.01/call, status unknown (last checked 2026-10-12).

Prices European call/put options using Black-Scholes-Merton and returns the option premium plus analytic Greeks (delta, gamma, theta, vega, rho), paid per-call via USDC on Solana or Base.

Price / call$0.01

Seller volume →—

Success—

StatusUnknown

How this service works

When to use: you already have model inputs (S or forward mark, K, T, r, σ) and need fair value + hedge ratios — not market-premium IV. European BSM price + analytic Greeks (delta, gamma, vega, theta, rho). Works for equity spots and power/commodity forwards (use the maturity mark as spot). USDC exact on Solana/Base. Free fixed sample: GET /v1/demo/option-price.

Output

A JSON object containing the Black-Scholes-Merton option price in spot currency units, a full analytic Greeks set (delta, gamma, theta per year, vega per unit vol, rho per unit rate), the echoed input parameters, the model name, a UUID request ID, and a UTC computation timestamp.

Example use cases

Equity option fair value check

“What's the Black-Scholes price and Greeks for a European put on a stock trading at $82.25, with a $85 strike, 45% implied vol, 3 months to expiry, 5% risk-free rate, and a 2% dividend yield?”

FX option delta hedging

“I need to delta-hedge a European call on EURUSD — spot is 1.08, strike is 1.10, vol is 12%, 6 months to expiry, USD rate 5.3%, EUR rate 3.8% as the dividend yield. What's the delta and full Greeks breakdown?”

Index call for portfolio scenario

“Price a 1-year European call on the S&P 500 index at spot 5200 with a 5250 strike, 18% vol, 4.5% rate, and 1.5% dividend yield — I want the option price and all analytic Greeks including theta and vega.”

Technical details

Endpoint

POSThttps://derivatives-pricer-production.up.railway.app/v1/option/price?utm_source=zero.xyz

When to prefer

Choose this endpoint when you need fast, analytic Black-Scholes pricing and exact closed-form Greeks for vanilla European options — it's ideal for real-time hedging calculations, scenario analysis, or educational tooling where an analytical solution suffices. Prefer it over Monte Carlo or finite-difference APIs when you need speed, reproducibility, and precise analytic Greeks without numerical noise. It is not suitable for American options, barrier options, or instruments requiring path-dependent simulation.

Side effects

Invalid or zero spot/strike/volatility — returns 400 with validation error
timeToExpiry set to 0 for an in-the-money option — returns intrinsic value with zero Greeks
Payment not processed or insufficient USDC balance — returns 402 Payment Required
Missing required fields (e.g. optionType, spot, strike) — returns 400 schema validation error
Extremely deep in/out-of-the-money with near-zero expiry — numerical edge cases may yield near-zero Greeks

Input

Schema · Request body

Field	Type	Description
rate	number	Continuously compounded risk-free rate r (e.g. 0.05 = 5%). For futures-style early exercise set r≈dividendYield.
spot	number	Underlying price S (> 0). Equity spot OR power/commodity forward mark for the option's window.
model	string	Pricing model: "bsm" (default European BSM on spot) or "black76" (forward/futures).
strike	number	Strike price K (> 0) in the same units as spot.
forward	number	Forward mark F for model=black76 (preferred). If omitted, spot is used as F.
treeSteps	integer	CRR steps for American (default 200 on single price).
expiration	string	ISO-8601 end of vol/exercise window. Mutually exclusive with timeToExpiry.
optionType	string	Call or put.
volatility	number	Annualized volatility σ as a decimal (> 0). Applies over the vol-accrual window τ.
optionStyle	string	Exercise style (default "european"). American uses CRR binomial with early exercise.
forwardStart	string	ISO-8601 start of vol/exercise window. If ≤ now, behaves like plain option to expiration.
timeToExpiry	number	Time to expiry T in years (≥ 0). Required unless expiration is set. Mutually exclusive with expiration.
dividendYield	number	Continuous dividend / convenience / yield q (≥ 0, default 0).
greekConvention	string	Greek units: "raw" (vega/1.0 vol, theta/year, rho/1.0 rate) or "trading" (vega/1%, theta/day, rho/bp).

Output

Schema · Response

{
  "type": "json",
  "example": {
    "model": "black-scholes-merton",
    "price": 10.45057562,
    "units": {
      "rho": "dV/dr per 1.0 absolute rate (not per 1%)",
      "vega": "dV/dσ per 1.0 absolute volatility (not per 1%)",
      "delta": "dV/dS or dV/dF (share / forward equivalent)",
      "gamma": "d²V/dS² or d²V/dF²",
      "price": "option value in spot/forward currency units",
      "theta": "dV/dT per year (not per day)"
    },
    "greeks": {
      "rho": 53.23248343,
      "vega": 37.52403469,
      "delta": 0.63683059,
      "gamma": 0.01876202,
      "theta": -6.41402764
    },
    "inputs": {
      "rate": 0.05,
      "spot": 100,
      "model": "bsm",
      "strike": 100,
      "optionType": "call",
      "volatility": 0.2,
      "optionStyle": "european",
      "timeToExpiry": 1,
      "dividendYield": 0,
      "greekConvention": "raw"
    },
    "timeline": {
      "tauYears": 1,
      "yearBasis": "ACT/365.25",
      "expiration": "2027-01-01T06:00:00.000Z",
      "forwardStart": "2026-01-01T00:00:00.000Z",
      "effectiveStart": "2026-01-01T00:00:00.000Z",
      "calendarYearsToExpiry": 1
    },
    "requestId": "00000000-0000-4000-8000-000000000001",
    "computedAt": "2026-01-01T00:00:00.000Z",
    "optionStyle": "european",
    "greeksQuality": "analytic",
    "greekConvention": "raw"
  }
}

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