# Black-Scholes Option Pricing & Greeks Calculator

> Black-Scholes Option Pricing & Greeks Calculator is a paid API for AI agents from x402-services-production.up.railway.app, paid per call via x402, $0.05/call, status unknown (last checked 2026-09-14).

Computes fair value and full Greeks (delta, gamma, vega, theta, rho) for any option using Black-Scholes, including unlisted strikes and crypto options

## Facts

- Endpoint: POST https://x402-services-production.up.railway.app/api/options/greeks
- Price: $0.05/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/black-scholes-option-pricing-greeks-calculator-33f7050d
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_eUIZFPxuRlBxFKS4-qUgJ

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-pricing-greeks-calculator-33f7050d -d '<json body>'
```

Example prompt: Use Black-Scholes to price a call option on ETH where the spot is $3,200, strike is $3,500, implied volatility is 75%, 30 days to expiry, and a risk-free rate of 0 — give me the fair value and all the greeks.

## When to prefer this

Choose this endpoint when you need to price any option — especially non-standard, OTC, or crypto options at arbitrary strikes not listed on exchanges. Ideal for quickly computing fair value and risk sensitivities without running your own Black-Scholes model. Best for crypto options where exchange-listed strikes may be limited.

## Known failure modes

- Missing required fields (type, spot, strike, daysToExpiry, iv) returns 400 error
- Invalid option type (not 'call' or 'put') causes rejection
- Negative or zero values for spot, strike, or iv may cause mathematical errors
- daysToExpiry of 0 can cause division-by-zero in Black-Scholes formula
- Payment not included or insufficient USDC results in 402 Payment Required

## How this service works

Black-Scholes option pricing: fair value + full greeks (delta, gamma, vega, theta, rho) for ANY option, listed or not. Send { type, spot, strike, daysToExpiry, iv, rate? }. Price any crypto option, not just exchange-listed strikes.

## Output

Returns the Black-Scholes theoretical fair value plus a full set of Greeks: delta (price sensitivity to underlying), gamma (rate of delta change), vega (sensitivity to IV), theta (time decay), and rho (sensitivity to interest rate) for the specified option parameters.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "daysToExpiry",
  "iv",
  "spot",
  "strike",
  "type"
 ],
 "properties": {
  "iv": {
   "type": "number",
   "description": "Implied volatility in % (e.g. 55)"
  },
  "rate": {
   "type": "number",
   "description": "Risk-free rate (default 0)"
  },
  "spot": {
   "type": "number",
   "description": "Underlying spot price"
  },
  "type": {
   "type": "string",
   "description": "call or put"
  },
  "strike": {
   "type": "number",
   "description": "Strike price"
  },
  "daysToExpiry": {
   "type": "number",
   "description": "Days to expiry"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/black-scholes-option-pricing-greeks-calculator-33f7050d/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from x402-services-production.up.railway.app](https://www.zero.xyz/host/x402-services-production.up.railway.app/llms.txt)