# Option Pricer & Greeks (Black-Scholes)

> Option Pricer & Greeks (Black-Scholes) is a paid API for AI agents from bess-x402.onrender.com, paid per call via x402, $0.002/call, status unknown (last checked 2026-10-30).

Calculates Black-Scholes price, Greeks (delta, gamma, vega, theta, rho), probability in the money, and breakeven for European call/put options, or solves for implied volatility from a market price.

## Facts

- Endpoint: GET https://bess-x402.onrender.com/v1/finance/option-price?utm_source=zero.xyz
- Price: $0.002/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-30
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/option-pricer-greeks-black-scholes-5cb37563
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_8eAvJtZUXoKR1_yW6XQvi

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 option-pricer-greeks-black-scholes-5cb37563
```

Example prompt: Price a European call option on a stock trading at $150, with a $155 strike, 30 days to expiry, and 25% annual volatility at a 4% risk-free rate — give me the Black-Scholes price and all the Greeks.

## When to prefer this

Use this endpoint when you need a fast, per-call, parameterized Black-Scholes pricer for European options across stocks, FX, or crypto without setting up a local quantitative library. It is ideal when you also need the full Greek surface and probability metrics in a single call. Prefer this over general-purpose data providers when you need implied volatility solved from a live market price.

## Known failure modes

- Missing required parameters (spot, strike, days) returns a 400 error
- Non-positive spot, strike, or days values may produce invalid results
- Implied volatility solver may fail to converge if market_price is far from theoretical bounds
- Negative implied volatility request when market price is below intrinsic value

## How this service works

Black-Scholes price and greeks (delta, gamma, vega, theta, rho) of a European call or put, probability in the money and breakeven; or the implied volatility from a market price. For stocks, FX or crypto.

## Output

Returns the theoretical option price (premium), all five Greeks (delta, gamma, vega, theta, rho), probability of expiring in the money, and the breakeven price. When a market_price is supplied instead of volatility, it returns the implied volatility that matches the observed price.

## 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",
      "HEAD",
      "DELETE"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "spot",
      "strike",
      "days"
     ],
     "properties": {
      "days": {
       "type": "number",
       "description": "Days to expiry"
      },
      "kind": {
       "type": "string",
       "description": "call or put"
      },
      "spot": {
       "type": "number",
       "description": "Underlying price"
      },
      "strike": {
       "type": "number",
       "description": "Strike price"
      },
      "rate_pct": {
       "type": "number",
       "description": "Risk-free rate in % (default 4)"
      },
      "market_price": {
       "type": "number",
       "description": "Option market price, to solve for implied volatility"
      },
      "volatility_pct": {
       "type": "number",
       "description": "Annual volatility in % (omit when giving market_price)"
      },
      "dividend_yield_pct": {
       "type": "number",
       "description": "Dividend or carry yield in %"
      }
     }
    }
   },
   "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/option-pricer-greeks-black-scholes-5cb37563/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from bess-x402.onrender.com](https://www.zero.xyz/host/bess-x402.onrender.com/llms.txt)