# Black-Scholes Option Pricer & Greeks Calculator

> Black-Scholes Option Pricer & Greeks Calculator is a paid API for AI agents from api.edifiedlab.com, paid per call via x402, $0.011/call, status unknown (last checked 2026-09-19).

Computes Black-Scholes option price and Greeks (delta, gamma, vega, theta) for European calls or puts given spot, strike, time-to-expiry, and volatility

## Facts

- Endpoint: POST https://api.edifiedlab.com/v1/market/black-scholes
- Price: $0.011/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-19
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/black-scholes-option-pricer-greeks-calculator-3d018356
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_3m1Ci6tuAsc91819PKBZ6

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-option-pricer-greeks-calculator-3d018356 -d '<json body>'
```

Example prompt: What's the Black-Scholes price and Greeks for a call option where the stock is trading at $150, the strike is $155, it expires in 3 months, annualized vol is 25%, and the risk-free rate is 4%?

## When to prefer this

Choose this endpoint when you need a fast, pure closed-form Black-Scholes computation with no dependency on live market data — ideal for options pricing bots, hedging calculators, or backtesting pipelines where you already have your own spot price and volatility inputs. Prefer this over broker APIs when you want a lightweight, deterministic calculation without authentication overhead or market-data subscriptions. Note that vega is returned per 1.0 volatility unit (not per 1%), so divide by 100 if you need per-1%-vol sensitivity.

## Known failure modes

- Missing required fields (spot, strike, tau, sigma, is_call) returns a 4xx validation error
- Non-positive spot or strike values rejected due to exclusiveMinimum:0 constraint
- Negative tau or sigma values rejected due to minimum:0 constraint
- Extreme inputs (very deep in/out of the money, near-zero tau) may produce numerically degenerate Greeks such as near-zero vega or very large gamma
- Payment failure (insufficient USDC balance) via x402 protocol returns 402 status before computation

## How this service works

Black-Scholes option price and Greeks (delta, gamma, vega, theta) from JSON keys spot, strike, tau (years; 3-month = 0.25), sigma (annualized volatility), and is_call (boolean). Pure closed-form calculation, no market data looked up or stored. vega is ∂price/∂sigma per 1.0 volatility (not per 1%).

## Output

Returns the theoretical option price and the four primary Greeks: delta (∂price/∂spot), gamma (∂²price/∂spot²), vega (∂price/∂sigma per 1.0 volatility unit, not per 1%), and theta (∂price/∂time). All values are derived purely from the closed-form Black-Scholes formula with no market data fetched or stored.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "tau": {
   "type": "number",
   "minimum": 0,
   "description": "time to expiry in years (3-month = 0.25)"
  },
  "rate": {
   "type": "number",
   "default": 0,
   "description": "annualized risk-free rate (optional; default 0)"
  },
  "spot": {
   "type": "number",
   "exclusiveMinimum": 0
  },
  "sigma": {
   "type": "number",
   "minimum": 0,
   "description": "annualized volatility"
  },
  "strike": {
   "type": "number",
   "exclusiveMinimum": 0
  },
  "is_call": {
   "type": "boolean",
   "description": "true for a call, false for a put"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/black-scholes-option-pricer-greeks-calculator-3d018356/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from api.edifiedlab.com](https://www.zero.xyz/host/api.edifiedlab.com/llms.txt)