# Black-Scholes European Option Calculator (Price, Greeks, IV)

> Black-Scholes European Option Calculator (Price, Greeks, IV) is a paid API for AI agents from api.agentstools.dev, paid per call via x402, $0.003/call, status unknown (last checked 2026-10-11).

Computes Black-Scholes fair price, all Greeks (delta, gamma, vega, theta, rho), or implied volatility for a European option given market parameters.

## Facts

- Endpoint: GET https://api.agentstools.dev/quant/options?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-11
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/black-scholes-european-option-calculator-price-greeks-iv-fa531774
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_Qq22MrUG40X1IiEi7zHH_

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-european-option-calculator-price-greeks-iv-fa531774
```

Example prompt: Using Black-Scholes, give me the full greeks for a European call option with spot price $150, strike $155, 0.25 years to expiry, risk-free rate 5%, and implied vol of 20%.

## When to prefer this

Use this endpoint when you need fast, pure-computation Black-Scholes analytics for European options — pricing, full Greek sensitivities, or implied volatility inversion — without requiring a brokerage account or market data subscription. Ideal for quant agents doing real-time derivatives analysis, hedging calculations, or risk management tasks.

## Known failure modes

- Missing required parameters (op, S, K, T, r) returns a 400 error
- sigma not provided for price or greeks operation returns an error
- market_price not provided for iv operation returns an error
- Non-positive values for S, K, or T return a validation error
- IV solve fails to converge if market_price is outside arbitrage bounds
- Payment not included or insufficient USDC returns 402 Payment Required

## How this service works

Black-Scholes European option calculator: fair price, all greeks (delta, gamma, vega, theta, rho), or implied volatility from a market price. Pure computation over your inputs.

## Output

Returns a JSON object containing the computed result(s) for the requested operation: for 'price' — the Black-Scholes fair value; for 'greeks' — the fair price plus delta, gamma, vega, theta, and rho; for 'iv' — the implied volatility solved from the observed market 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": [
      "op",
      "S",
      "K",
      "T",
      "r"
     ],
     "properties": {
      "K": {
       "type": "number",
       "description": "Strike price (> 0)"
      },
      "S": {
       "type": "number",
       "description": "Spot price of the underlying (> 0)"
      },
      "T": {
       "type": "number",
       "description": "Time to expiry in years (> 0)"
      },
      "q": {
       "type": "number",
       "description": "Continuous dividend yield as a decimal, default 0"
      },
      "r": {
       "type": "number",
       "description": "Risk-free rate, continuous, as a decimal"
      },
      "op": {
       "enum": [
        "price",
        "greeks",
        "iv"
       ],
       "type": "string",
       "description": "price returns the fair value; greeks returns price plus all greeks; iv solves for implied volatility"
      },
      "type": {
       "enum": [
        "call",
        "put"
       ],
       "type": "string",
       "description": "Option type, default call"
      },
      "sigma": {
       "type": "number",
       "description": "Volatility as a decimal (needed for price and greeks)"
      },
      "market_price": {
       "type": "number",
       "description": "Observed option price, used for op=iv instead of sigma"
      }
     }
    }
   },
   "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-european-option-calculator-price-greeks-iv-fa531774/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from api.agentstools.dev](https://www.zero.xyz/host/api.agentstools.dev/llms.txt)