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Black-Scholes-Merton European Option Pricer with Greeks
x402
Black-Scholes-Merton European Option Pricer with Greeks is a paid API for AI agents from agent402.tools, paid per call via x402, $0.002/call, status unknown (last checked 2026-09-15).
Prices a European call or put option using the Black-Scholes-Merton model and returns the option price plus all five Greeks (delta, gamma, vega, theta, rho), with support for continuous dividend yield.
Price / call$0.002
Success—
StatusUnknown
How this service works
Price a European option (call or put) with the Black-Scholes-Merton model, plus the greeks (delta, gamma, vega, theta, rho). Continuous dividend yield supported. Greeks are per unit: theta is per year, vega per 1.00 change in volatility, rho per 1.00 change in rate. Deterministic - matches standard references to the cent.
Output
Returns the theoretical fair value of the European option and all five Greeks: delta (price sensitivity to spot), gamma (rate of change of delta), vega (sensitivity to 1.00 change in volatility), theta (time decay per year), and rho (sensitivity to interest rate per 1% change).
Example use cases
Example prompt
“Use Black-Scholes to price a European call option on a stock trading at $150, with a strike of $155, 30% annual volatility, a risk-free rate of 5%, dividend yield of 1.5%, expiring in 0.5 years — and give me all the greeks.”
Technical details
Endpoint
POSThttps://agent402.tools/api/black-scholesWhen to prefer
Use this endpoint when you need a fast, analytically exact Black-Scholes-Merton price and full set of Greeks for a European option, especially when continuous dividend yield is relevant. Prefer this over Monte Carlo or binomial tree services when speed and closed-form accuracy matter and the option has no early exercise (American-style) features.
Side effects
- Missing required fields (spot, strike, type, volatility, riskFreeRate, timeToExpiryYears) returns a 400 error
- Invalid option type string (not 'call' or 'put') returns a validation error
- Non-positive spot or strike price may cause computation errors
- Negative timeToExpiryYears is mathematically undefined
- Extreme parameter values (e.g., very high volatility) may produce numerical edge cases
- Payment failure (insufficient USDC balance or x402 wallet not configured) blocks the call
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| spot | number | Current underlying price (S) |
| type | string | "call" or "put" |
| strike | number | Strike price (K) |
| volatility | number | Annual volatility as decimal (sigma) |
| riskFreeRate | number | Annual risk-free rate as decimal (r) |
| dividendYield | number | Continuous dividend yield as decimal (q). Default 0. |
| timeToExpiryYears | number | Time to expiry in years (T) |
Output
Schema · Response
{
"type": "json",
"example": {
"d1": 0.35,
"d2": 0.15,
"rho": 53.2325,
"type": "call",
"vega": 37.524,
"delta": 0.6368,
"gamma": 0.0188,
"price": 10.4506,
"theta": -6.414
}
}Tags
x402
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