# Black-Scholes European Option Calculator

> Black-Scholes European Option Calculator is a paid API for AI agents from payai.agentstools.dev, paid per call via x402, $0.003/call, status unknown (last checked 2026-10-12).

Computes Black-Scholes fair price, all Greeks (delta, gamma, vega, theta, rho), or implied volatility for European options given spot price, strike, time to expiry, rate, and volatility.

## Facts

- Endpoint: GET https://payai.agentstools.dev/quant/options?utm_source=zero.xyz
- Price: $0.003/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-european-option-calculator-c0184009
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_K3O67yxYNRzqF-6KJttQW

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-c0184009
```

Example prompt: Use Black-Scholes to price a European call option where the spot price is $150, strike is $155, time to expiry is 0.5 years, risk-free rate is 5%, and volatility is 20% — give me the fair value and all the Greeks.

## When to prefer this

Use this endpoint when you need fast, pure-compute Black-Scholes analytics for European options — fair pricing, Greeks, or implied volatility — without any market data dependencies. Prefer it over general financial APIs when you already have your own inputs and just need the mathematical result.

## Known failure modes

- Missing required parameters (op, S, K, T, r) returns a 400 error
- Sigma not provided when op=price or op=greeks returns an error
- Market_price not provided when op=iv returns an error
- Non-positive values for S, K, or T cause computation errors
- Implied volatility solver may fail to converge for extreme or nonsensical market prices

## 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 the Black-Scholes fair price and/or Greeks (delta, gamma, vega, theta, rho) for a European option, or the implied volatility solved from an observed market price, depending on the 'op' parameter chosen (price, greeks, or iv).

## 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-c0184009/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from payai.agentstools.dev](https://www.zero.xyz/host/payai.agentstools.dev/llms.txt)