# AgentsToolsHub European Option Pricing (Black-Scholes-Merton)

> AgentsToolsHub European Option Pricing (Black-Scholes-Merton) is a paid API for AI agents from agentstoolshub.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-10-17).

Computes exact European option price (call or put) and all five Greeks (delta, gamma, theta, vega, rho) using the Black-Scholes-Merton closed-form model, with optional dividend yield support.

## Facts

- Endpoint: GET https://agentstoolshub.com/api/v1/finance/option-price?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-17
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/agentstoolshub-european-option-pricing-black-scholes-merton-53ab4db2
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_zXCqCzTmKYlGkeaJOV3YN

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 agentstoolshub-european-option-pricing-black-scholes-merton-53ab4db2
```

Example prompt: What's the Black-Scholes price and all five Greeks for a European call option with a spot price of $150, strike of $155, 45 days to expiry, implied volatility of 28%, and a risk-free rate of 5%?

## When to prefer this

Use this endpoint when you need exact, deterministic European option pricing via the Black-Scholes-Merton closed-form model rather than numerical approximations or simulation. Ideal when all five Greeks are needed simultaneously alongside the price. Prefer this over Monte Carlo or binomial tree approaches when the option is European-style (no early exercise) and when speed and determinism matter. The dividend yield parameter makes it suitable for equity options on dividend-paying stocks.

## Known failure modes

- Missing required parameters (spot, strike, years, volPct) returns a 400 error
- Negative or zero time-to-expiry may produce undefined or degenerate outputs
- Extremely high or low volatility values may produce near-boundary pricing
- Non-numeric query parameter values return validation errors
- Invalid option type (not 'call' or 'put') returns an enum validation error

## How this service works

European option pricing with the Black-Scholes-Merton model: exact price for calls and puts plus delta, gamma, theta, vega and rho, with dividend yield support. Deterministic closed-form math — the numbers agents should quote instead of hallucinating option values. Use this when an agent needs to black-Scholes price + all five Greeks.

## Output

Returns the theoretical price of the European option (call or put) and all five Greeks: delta (price sensitivity to spot), gamma (rate of change of delta), theta (time decay), vega (sensitivity to volatility), and rho (sensitivity to interest rates), computed via the exact Black-Scholes-Merton closed-form formula.

## 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",
      "years",
      "volPct"
     ],
     "properties": {
      "spot": {
       "type": "number",
       "description": "Spot price"
      },
      "type": {
       "enum": [
        "call",
        "put"
       ],
       "type": "string",
       "description": "Type"
      },
      "years": {
       "type": "number",
       "description": "Time to expiry (years)"
      },
      "strike": {
       "type": "number",
       "description": "Strike"
      },
      "volPct": {
       "type": "number",
       "description": "Volatility (%)"
      },
      "ratePct": {
       "type": "number",
       "description": "Risk-free rate (%)"
      },
      "divYieldPct": {
       "type": "number",
       "description": "Dividend yield (%)"
      }
     }
    }
   },
   "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/agentstoolshub-european-option-pricing-black-scholes-merton-53ab4db2/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from agentstoolshub.com](https://www.zero.xyz/host/agentstoolshub.com/llms.txt)