# 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 2026-09-13).

Computes European call/put fair value and Greeks (delta, gamma, theta, vega, rho) from spot, strike, days-to-expiry, rate, and volatility; optionally solves for implied volatility given a market price.

## Facts

- Endpoint: POST https://api.24klabs.ai/api/v1/black-scholes-options-pricer
- Price: $0.005/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-13
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/black-scholes-options-pricer-86e7ae66
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_BfzIt6mN2E0CsWMCX_Qe5

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-86e7ae66 -d '<json body>'
```

Example prompt: Price 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 — give me the fair value and all the Greeks.

## When to prefer this

Use this endpoint when you need a fast, server-side Black-Scholes calculation without running your own math library — particularly useful in agent workflows that need option fair value or Greeks on demand, or when you want implied volatility solved from a live market price without implementing Newton-Raphson yourself. Prefer this over general-purpose computation endpoints because it handles all five Greeks and IV solve in a single call.

## Known failure modes

- Missing required parameters (spot, strike, days-to-expiry, rate, or volatility) return a 400 validation error
- Volatility or rate supplied as zero or negative may cause numerical instability or division errors
- Implied vol solve may fail to converge if the market_price is outside arbitrage bounds (e.g. below intrinsic value or above spot)
- Very short days-to-expiry (near zero) can produce extreme Greeks values
- Invalid option type string (not 'call' or 'put') returns a parameter 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 option's fair value (theoretical price), plus the five standard Greeks: delta (price sensitivity to spot), gamma (delta sensitivity to spot), theta (time decay per day), vega (sensitivity to volatility), and rho (sensitivity to interest rate). If a market_price is supplied, also returns the implied volatility solved iteratively to match that market 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-86e7ae66/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)