# Black-Scholes / Black-76 Options Greeks & Implied Volatility Calculator

> Black-Scholes / Black-76 Options Greeks & Implied Volatility Calculator is a paid API for AI agents from cryptopulse.theaslangroupllc.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-11).

Computes Black-Scholes or Black-76 options price, all greeks (delta, gamma, vega, theta, rho), intrinsic/time value, and breakeven — or solves implied volatility from a given market price — with CDF accuracy to 1e-15.

## Facts

- Endpoint: GET https://cryptopulse.theaslangroupllc.com/api/options-greeks?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-11
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/black-scholes-black-76-options-greeks-implied-volatility-calculator-6848e10d
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_4ytFUclg1I5FBfklV5ZXO

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability black-scholes-black-76-options-greeks-implied-volatility-calculator-6848e10d
```

Example prompt: What are the full greeks and implied vol for a call option where spot is 3200, strike is 3400, expiry is 2025-09-19, and the current market price is 85 — use Black-Scholes?

## When to prefer this

Use this endpoint when you need fast, deterministic, high-precision options math without any external market data dependency — ideal for pricing checks, greek calculations, implied vol extraction, or building options analytics into an automated workflow. Prefer this over LLM-based or data-vendor approaches when reproducibility and mathematical accuracy are required. Not suitable for fetching live market prices or volatility surfaces.

## Known failure modes

- Missing required parameters (spot/forward, strike, expiry) returns a 4xx error
- Invalid expiry format (non-ISO date, non-numeric years) causes a parse error
- Negative or zero spot/strike values may return an error or undefined result
- If solving implied vol and the supplied price is outside theoretical bounds, convergence may fail
- Ambiguous model selection (Black-Scholes vs Black-76) if forward vs spot not clearly specified

## How this service works

Options pricing and greeks calculator, deterministic. Answers "what are the greeks for this option", "what is the implied vol of this price". Buyer supplies spot or forward, strike, expiry (ISO date or years), and iv or price; returns Black-Scholes or Black-76 price, delta, gamma, vega, theta, rho, intrinsic/time value, breakeven — or the implied vol solved from price. Pure math (normal CDF accurate to 1e-15), no data source, no LLM, no key.

## Output

Returns a JSON object containing the option price (Black-Scholes or Black-76), delta, gamma, vega, theta, rho, intrinsic value, time value, breakeven price, and — if solving from a market price — the implied volatility. All values are computed deterministically using high-precision normal CDF (accurate to 1e-15). No external data sources are involved.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "type",
  "strike"
 ],
 "properties": {
  "q": {
   "type": "number",
   "description": "annualized dividend/borrow yield, decimal (Black-Scholes only, default 0)"
  },
  "r": {
   "type": "number",
   "description": "annualized risk-free rate, decimal (default 0)"
  },
  "t": {
   "type": "number",
   "description": "years to expiry (alternative to expiry)"
  },
  "iv": {
   "type": "number",
   "description": "annualized vol, decimal or percent (0.62 or 62) — provide iv OR price"
  },
  "spot": {
   "type": "number",
   "description": "spot price (Black-Scholes mode; provide spot OR forward)"
  },
  "type": {
   "type": "string",
   "description": "call | put"
  },
  "price": {
   "type": "number",
   "description": "option price to solve implied vol from (alternative to iv)"
  },
  "expiry": {
   "type": "string",
   "description": "ISO expiry date (08:00 UTC assumed) — or pass t instead"
  },
  "strike": {
   "type": "number",
   "description": "strike price"
  },
  "forward": {
   "type": "number",
   "description": "forward/futures price (Black-76 mode — the crypto-venue convention)"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "model": "black76",
  "greeks": {
   "delta": 0.298,
   "gamma": 0.00063,
   "price": 41.18,
   "theta_per_day": -1.91,
   "vega_per_vol_point": 2.68
  },
  "inputs": {
   "t": 0.05,
   "iv": 0.71,
   "type": "call",
   "strike": 3600,
   "forward": 3450
  },
  "deterministic": true
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/black-scholes-black-76-options-greeks-implied-volatility-calculator-6848e10d/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from cryptopulse.theaslangroupllc.com](https://www.zero.xyz/host/cryptopulse.theaslangroupllc.com/llms.txt)