# Saylor Innovations Data Desk: Black-Scholes Option Pricer

> Saylor Innovations Data Desk: Black-Scholes Option Pricer is a paid API for AI agents from saylorinnovations.com, paid per call via x402, $0.01/call, status unknown (last checked 2026-10-18).

Calculates Black-Scholes-Merton theoretical price and full Greeks (delta, gamma, vega, theta, rho) for European call or put options, plus intrinsic/time value breakdown, moneyness, and put-call parity check

## Facts

- Endpoint: GET https://saylorinnovations.com/api/finance/black-scholes?utm_source=zero.xyz
- Price: $0.01/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-18
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/saylor-innovations-data-desk-black-scholes-option-pricer-32774958
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_2ZlXSOJvkO-U9NvGCZPg8

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 saylor-innovations-data-desk-black-scholes-option-pricer-32774958
```

Example prompt: What's the Black-Scholes price and Greeks for a call option with a spot price of $150, strike of $155, 6 months to expiry, 25% volatility, and a 4% risk-free rate?

## When to prefer this

Choose this endpoint when you need a fast, cheap ($0.01), theoretically rigorous Black-Scholes-Merton price and full Greeks suite for European-style options in a single API call. It is ideal for agents performing real-time options analysis, hedging calculations, portfolio risk assessment, or educational finance tasks. Prefer it over generic financial data APIs when you need computed derivatives metrics (Greeks) rather than market-observed prices, and over building your own BSM implementation when you want a validated, hosted computation with put-call parity sanity checking included.

## Known failure modes

- Missing required parameters (s, k, t, sigma) returns an error — all four are mandatory
- Invalid or non-numeric values for spot, strike, time, or volatility cause computation failure
- Time to expiry of 0 or negative values may produce undefined or null Greek values
- Extremely deep in-the-money or out-of-the-money options may return null Greeks due to numerical precision limits
- Risk-free rate defaults to 0.04 if omitted; forgetting to pass it explicitly may produce unexpected pricing
- Option type defaults to 'call' if omitted — omitting 'type=put' will silently price a call instead

## How this service works

Black-Scholes-Merton price for European calls and puts with delta, gamma, vega, theta, rho, intrinsic and time value, moneyness and put-call parity check

## Output

Returns a JSON object with: the theoretical option price, Black-Scholes d1 and d2 intermediate terms, a full Greeks breakdown (delta, gamma, vega per volatility point, theta per day, rho per rate point), intrinsic value, time value, moneyness classification, a put-call parity check, and a note with contextual caveats about interpreting the result.

## 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": [
      "s",
      "k",
      "t",
      "sigma"
     ],
     "properties": {
      "k": {
       "type": "string",
       "description": "Strike price"
      },
      "r": {
       "type": "string",
       "description": "optional risk-free rate decimal, default 0.04"
      },
      "s": {
       "type": "string",
       "description": "Spot price"
      },
      "t": {
       "type": "string",
       "description": "Years to expiry (0.5 = six months)"
      },
      "type": {
       "type": "string",
       "description": "call (default) or put"
      },
      "sigma": {
       "type": "string",
       "description": "Volatility as a decimal (0.25 = 25%)"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "json"
    },
    "example": {
     "type": "object",
     "required": [
      "inputs",
      "price",
      "greeks"
     ],
     "properties": {
      "d1": {
       "type": [
        "number",
        "null"
       ],
       "description": "Black-Scholes d1 term"
      },
      "d2": {
       "type": [
        "number",
        "null"
       ],
       "description": "Black-Scholes d2 term"
      },
      "note": {
       "type": "string",
       "description": "Caveat or context for reading the result"
      },
      "price": {
       "type": "number",
       "description": "Price"
      },
      "greeks": {
       "type": "object",
       "properties": {
        "delta": {
         "type": [
          "number",
          "null"
         ],
         "description": "Option price change per 1 change in the underlying"
        },
        "gamma": {
         "type": [
          "number",
          "null"
         ],
         "description": "Change in delta per 1 change in the underlying"
        },
        "theta_per_day": {
         "type": [
          "number",
          "null"
         ],
         "description": "Theta per day"
        },
        "rho_per_rate_point": {
    
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/saylor-innovations-data-desk-black-scholes-option-pricer-32774958/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from saylorinnovations.com](https://www.zero.xyz/host/saylorinnovations.com/llms.txt)