# Black-Scholes Options Pricer

> Black-Scholes Options Pricer is a paid API for AI agents from api.24klabs.ai, paid per call via x402, $0.005/call, status unknown (last checked 2026-10-12).

Prices European call/put options (fair value + Greeks) using Black-Scholes, with optional implied volatility solve from a market price.

## Facts

- Endpoint: POST https://api.24klabs.ai/api/black-scholes-options-pricer?utm_source=zero.xyz
- Price: $0.005/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-options-pricer-949a3559
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_rE8D1XvD-TqKBFOBmARnG

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-949a3559 -d '<json body>'
```

Example prompt: What's the Black-Scholes fair value and all the Greeks for a European call option with a spot price of $150, strike of $155, 45 days to expiry, 5% risk-free rate, and 25% implied volatility?

## When to prefer this

Choose this endpoint when you need fast, reliable Black-Scholes pricing and Greeks for European-style options without standing up your own quant library. Ideal for agents doing real-time hedging analysis, building risk reports, or extracting implied volatility from observed market prices. Not suitable for American options (which require binomial or finite-difference methods) or exotic payoffs.

## Known failure modes

- Missing required fields (spot, strike, DTE, rate, volatility) returns a 400 error
- Negative or zero spot/strike/DTE values may cause computation errors
- Extremely deep in-the-money or out-of-the-money options may produce near-zero Greeks with precision caveats
- Implied vol solve may fail to converge if market_price is below intrinsic value or otherwise arbitrage-free bounds are violated
- Payment failure (insufficient USDC balance or x402 auth issue) returns a 402 error

## How this service works

European call/put fair value plus delta, gamma, theta, vega, rho from spot, strike, days-to-expiry, rate and volatility; optional implied-vol solve if market_price supplied.

## Output

Returns the theoretical fair value of the European call or put option, plus the five standard Greeks: delta (directional sensitivity), gamma (delta curvature), theta (time decay), vega (volatility sensitivity), and rho (rate sensitivity). If a market_price is supplied, also returns the implied volatility solved from that price.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "rate": {
   "type": "number"
  },
  "spot": {
   "type": "number"
  },
  "type": {
   "type": "string"
  },
  "strike": {
   "type": "number"
  },
  "volatility": {
   "type": "number"
  },
  "days_to_expiry": {
   "type": "number"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "delta": 0.28,
  "gamma": 0.05,
  "price": 0.94
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/black-scholes-options-pricer-949a3559/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from api.24klabs.ai](https://www.zero.xyz/host/api.24klabs.ai/llms.txt)