# Black-Scholes Greeks

> Black-Scholes Greeks is a paid API for AI agents from 164.160.90.241.sslip.io, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-12).

Computes European option call and put prices plus all five Greeks (delta, gamma, vega, theta, rho) using the Black-Scholes model

## Facts

- Endpoint: GET https://164.160.90.241.sslip.io/api/math-black-scholes-greeks?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-12
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/black-scholes-greeks-f1bb5a81
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_0wx-qz6ggSu8tMsVPwpSa

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-greeks-f1bb5a81
```

Example prompt: Can you calculate the Black-Scholes price and all five Greeks for a European call and put with spot at 100, strike at 105, 0.25 years to expiry, a risk-free rate of 5%, and volatility of 20%?

## When to prefer this

Choose this endpoint when you need a fast, authoritative Black-Scholes calculation for European options covering all five Greeks in a single call. Prefer it over manual computation or general math sandboxes when you need structured, labeled outputs for delta, gamma, vega, theta, and rho alongside the option price. It is not suitable for American options (early exercise), exotic options, or models beyond Black-Scholes (e.g., binomial trees, Monte Carlo).

## Known failure modes

- Missing required parameters (spot, strike, time, rate, vol) returns a validation error
- Non-positive time to expiry or volatility may produce NaN or error responses
- Extreme parameter values (e.g., very deep in/out of the money) may produce near-zero or near-1 Greeks
- Network or upstream server unavailability returns HTTP 5xx
- Invalid non-numeric query parameter types return a 400 bad request

## How this service works

European option price (call and put) with delta, gamma, vega, theta and rho via Black-Scholes.

## Output

Returns the theoretical call and put prices calculated via Black-Scholes, along with all five Greeks: delta (price sensitivity to spot), gamma (rate of change of delta), vega (sensitivity to volatility), theta (time decay), and rho (sensitivity to interest rate), all as numeric values.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "spot",
      "strike",
      "time",
      "rate",
      "vol"
     ],
     "properties": {
      "vol": {
       "type": "number",
       "description": "Volatility as decimal"
      },
      "rate": {
       "type": "number",
       "description": "Risk-free rate as decimal"
      },
      "spot": {
       "type": "number",
       "description": "Underlying price"
      },
      "time": {
       "type": "number",
       "description": "Years to expiry"
      },
      "strike": {
       "type": "number",
       "description": "Strike"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object"
    }
   }
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/black-scholes-greeks-f1bb5a81/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from 164.160.90.241.sslip.io](https://www.zero.xyz/host/164.160.90.241.sslip.io/llms.txt)