Option Price (Black-Scholes)
European option pricing with the Black-Scholes-Merton model: exact price for calls and puts plus delta, gamma, theta, vega and rho, with dividend yield support. Deterministic closed-form math — the numbers agents should quote instead of hallucinating option values.
Worked examples
ATM 1y call, σ 20%
GET /api/v1/finance/option-price?type=call&spot=100&strike=100&years=1&volPct=20&ratePct=5
Result: 10.45 per call (σ 20%, T 1y)
6m put, σ 35%
GET /api/v1/finance/option-price?type=put&spot=100&strike=95&years=0.5&volPct=35&ratePct=5
Result: 6.26 per put (σ 35%, T 0.5y)
Deep OTM call with dividend
GET /api/v1/finance/option-price?type=call&spot=100&strike=140&years=1&volPct=25&ratePct=4&divYieldPct=2
Result: 1.4 per call (σ 25%, T 1y)
Machine API (x402)
$0.003 / callThis tool is also a JSON API for AI agents. Requests without payment receive 402 Payment Required plus instructions; agents pay USDC on Base via the x402 protocol — no accounts, no API keys.
GET /api/v1/finance/option-price?type=call&spot=100&strike=100&years=1&volPct=20&ratePct=5 HTTP/1.1
Host: agentstoolshub.com
→ 402 (payment required, instructions in headers)
→ 200 (after X-PAYMENT header; JSON body below)
{
"tool": "finance/option-price",
"input": {"type":"call","spot":100,"strike":100,"years":1,"volPct":20,"ratePct":5},
"result": { "value": 10.450575, "answer": "10.45 per call (σ 20%, T 1y)" }
}Agent docs: /llms.txt · OpenAPI spec · integration guide
About this tool
Black-Scholes-Merton closed-form pricing for European options with the full Greeks vector. Verified against textbook reference values, with dividend yield support. Deterministic by construction — identical inputs always return the identical price and Greeks.
C = S·e^(−qT)·N(d₁) − K·e^(−rT)·N(d₂), d₁ = (ln(S/K) + (r − q + σ²/2)T)/(σ√T)
Frequently asked questions
Does this work for American options?
No — Black-Scholes prices European exercise only. American puts on dividend-paying underlyings are worth more; use a binomial model for those.
What units are the Greeks in?
Delta and gamma are per $1 move; theta is per calendar day; vega is per 1 percentage-point of volatility; rho is per 1 percentage-point of interest rate.