BSM Greeks Calculator API

Endpoint

Computes full Black-Scholes-Merton greeks from the inputs you provide. Returns the theoretical price plus first-order, second-order and third-order greeks. Pure calculation - no market data required. Available on all plans (Free+).

Parameters

Request

curl -H "X-Api-Key: YOUR_API_KEY" \
  "https://lab.flashalpha.com/v1/pricing/greeks?spot=580&strike=580&dte=30&sigma=0.18&type=call"

import requests

resp = requests.get(
    "https://lab.flashalpha.com/v1/pricing/greeks",
    params={"spot": 580, "strike": 580, "dte": 30, "sigma": 0.18, "type": "call"},
    headers={"X-Api-Key": "YOUR_API_KEY"}
)
resp.raise_for_status()
g = resp.json()
print(f"Price {g['theoretical_price']} | delta {g['first_order']['delta']} | vanna {g['second_order']['vanna']}")

const qs = new URLSearchParams({ spot: 580, strike: 580, dte: 30, sigma: 0.18, type: "call" });
const resp = await fetch(`https://lab.flashalpha.com/v1/pricing/greeks?${qs}`, {
  headers: { "X-Api-Key": "YOUR_API_KEY" }
});
if (!resp.ok) throw new Error(`HTTP ${resp.status}`);
const g = await resp.json();
console.log(`Price ${g.theoretical_price} | delta ${g.first_order.delta}`);

{
  "inputs": {
    "spot": 580,
    "strike": 580,
    "dte": 30,
    "sigma": 0.18,
    "type": "call",
    "risk_free_rate": 0.045,
    "dividend_yield": 0.013
  },
  "theoretical_price": 12.6872,
  "first_order": {
    "delta": 0.53003,
    "gamma": 0.013276,
    "theta": -0.223599,
    "vega": 0.660706,
    "rho": 24.2244
  },
  "second_order": {
    "vanna": -0.055551,
    "charm": 0.00049,
    "vomma": 0.709126,
    "dual_delta": -0.508155
  },
  "third_order": {
    "speed": -0.000057,
    "zomma": -0.07361,
    "color": -0.000223,
    "ultima": -17.2416
  },
  "additional": {
    "lambda": 24.2305,
    "veta": 1.0923
  },
  "endpoint_version": "2026.09.30",
  "data_as_of": {
    "node": "fa5",
    "equity_feed": "2026-10-30T13:46:17.449Z",
    "equity_options_feed": "2026-10-30T13:46:17Z",
    "index_feed": "2026-10-30T13:46:16.137Z",
    "index_options_feed": "2026-10-30T13:46:16Z",
    "futures_feed": "2026-10-30T13:46:15.271Z",
    "futures_options_feed": "2026-10-30T13:46:14.335Z",
    "flow_feed": "2026-10-30T13:46:00Z",
    "oi_feed": "2026-10-29T20:00:00Z",
    "macro_feed": "2026-10-29T21:00:20Z"
  }
}

Response Fields

Errors

Authentication (401) and rate-limit (429) errors use the common error format, see Error Responses.

What Is the Greeks Calculator Endpoint?

The Greeks Calculator prices a European option with the Black-Scholes-Merton model from inputs you supply and returns every sensitivity in one response: the familiar first-order greeks, the second-order cross greeks (vanna, charm, vomma) that drive dealer hedging, and third-order greeks for convexity analysis. It never reads market data, so you can price hypothetical trades, stress inputs, or check your own pricer against a reference implementation.

Common Use Cases

• Price what-if trades - change spot, vol or days to expiry and read the new price and greeks
• Validate your own pricer - compare your BSM implementation against a reference output
• Study higher-order risk - read vanna, charm, speed and zomma for hedging and convexity work
• Build a calculator UI - back an options calculator without shipping pricing code to the client

Related

Related reading

• Build a BSM pricing tool with the greeks API - a worked calculator example
• Real-time options greeks API - greeks on live chains instead of your own inputs

Complementary endpoints

• Implied Volatility Solver - back out sigma from a market price first
• Kelly Position Sizing - size the trade once it is priced
• Option Quote - greeks for live listed contracts