# Black-Scholes Options Pricer & Greeks Calculator

> Black-Scholes Options Pricer & Greeks Calculator is a paid API for AI agents from x402helper.xyz, paid per call via x402, $0.004/call, status unknown (last checked 2026-10-31).

Computes fair value, Greeks (delta, gamma, theta, vega, rho), or implied volatility for European options using the Black-Scholes model.

## Facts

- Endpoint: GET https://x402helper.xyz/89e509/quant/options?utm_source=zero.xyz
- Price: $0.004/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-31
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/black-scholes-options-pricer-greeks-calculator-6d18ea61
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap__4px2yV7tCnw2SEpgg-w9

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-options-pricer-greeks-calculator-6d18ea61
```

Example prompt: Price a European call option where the stock is at $150, the strike is $155, it expires in 0.25 years, the risk-free rate is 5%, and volatility is 20% — give me the fair value.

## When to prefer this

Choose this endpoint when you need fast, mathematically rigorous Black-Scholes pricing, Greeks, or implied volatility for European options without standing up your own quant infrastructure. Ideal for AI agents that need on-demand options analytics at low cost ($0.004/call via x402 micropayments) without API keys or subscriptions.

## Known failure modes

- Missing required parameters (op, S, K, T, r) returns an error
- sigma missing when op=price or op=greeks (needed for computation)
- market_price missing when op=iv
- S, K, or T <= 0 (invalid domain) returns an error
- Non-numeric parameter values cause parsing errors
- Network or payment failure results in HTTP 402 if USDC not provided

## How this service works

X402 micropayments server — AI agents pay USDC for OFAC screening, rates, and billing verification.

## Output

Returns a JSON object with success=true and a result object containing the computed output: for op=price, the theoretical option price; for op=greeks, the price plus all Greeks (delta, gamma, theta, vega, rho); for op=iv, the implied volatility as a decimal.

## 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": [
      "op",
      "S",
      "K",
      "T",
      "r"
     ],
     "properties": {
      "K": {
       "type": "number",
       "default": null,
       "description": "Strike price (> 0)"
      },
      "S": {
       "type": "number",
       "default": null,
       "description": "Spot price of the underlying (> 0)"
      },
      "T": {
       "type": "number",
       "default": null,
       "description": "Time to expiry in years (> 0)"
      },
      "q": {
       "type": "number",
       "default": null,
       "description": "Continuous dividend yield as a decimal, default 0"
      },
      "r": {
       "type": "number",
       "default": null,
       "description": "Risk-free rate, continuous, as a decimal"
      },
      "op": {
       "enum": [
        "price",
        "greeks",
        "iv"
       ],
       "type": "string",
       "default": null,
       "description": "price returns the fair value; greeks returns price plus all greeks; iv solves for implied volatility"
      },
      "type": {
       "enum": [
        "call",
        "put"
       ],
       "type": "string",
       "default": null,
       "description": "Option type, default call"
      },
      "sigma": {
       "type": "number",
       "default": null,
       "description": "Volatility as a decimal (needed for price and greeks)"
      },
      "market_price": {
       "type": "number",
       "default": null,
       "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"
    }
   }
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "result": {},
  "success": true
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/black-scholes-options-pricer-greeks-calculator-6d18ea61/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from x402helper.xyz](https://www.zero.xyz/host/x402helper.xyz/llms.txt)