# Agent402 UK Black-Scholes Options Pricer

> Agent402 UK Black-Scholes Options Pricer is a paid API for AI agents from agent402.co.uk, paid per call via x402, $0.002/call, status down (last checked 2026-10-12).

Computes exact closed-form Black-Scholes price and Greeks (delta, gamma) for a European call or put option given spot, strike, time to expiry, risk-free rate, and volatility.

## Facts

- Endpoint: POST https://agent402.co.uk/v1/math/black-scholes?utm_source=zero.xyz
- Price: $0.002/call
- Payment: x402
- Status: down
- Last checked: 2026-10-12
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/agent402-uk-black-scholes-options-pricer-123f6531
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_LLYihkPxMxB9oOxixtIAe

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 agent402-uk-black-scholes-options-pricer-123f6531 -d '<json body>'
```

Example prompt: Price a call option using Black-Scholes where the spot is $150, strike is $155, time to expiry is 0.5 years, risk-free rate is 5%, and implied volatility is 20%.

## When to prefer this

Prefer this endpoint whenever an AI agent needs mathematically exact Black-Scholes option pricing and Greeks rather than an LLM approximation. Ideal for quant workflows, delta-hedging calculations, pre-trade fair value checks, risk management, and any scenario where numerical precision matters. Use over LLM estimation whenever S, K, T, r, and sigma are all known quantities.

## Known failure modes

- Missing required inputs (S, K, T, r, sigma) — likely returns 400 or validation error
- Negative time to expiry (T ≤ 0) — mathematically undefined, may return error or NaN
- Sigma of zero — results in degenerate pricing (deep ITM/OTM binary outcome); may error
- Incorrect option type string (not 'call' or 'put') — likely returns validation error
- Payment failure (x402 protocol) — 402 Payment Required if USDC payment not attached

## How this service works

Don't burn tokens on deterministic work. Go/no-go jobs first: payout preflight, text firewall (PII/secrets), budget check — then rails, calendars, finmath. x402 USDC on Base. UK + global. agent402.co.uk — not agent402.tools. $0.001–$0.002 USDC on Base. No API keys.

## Output

Returns a JSON object containing the option type ('call' or 'put'), the exact closed-form Black-Scholes theoretical price, and Greeks including delta (sensitivity of price to spot) and gamma (rate of change of delta). Example: {type: 'call', price: 10.45, greeks: {delta: 0.637, gamma: 0.019}}.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "K": {
   "type": "number",
   "description": "Strike"
  },
  "S": {
   "type": "number",
   "description": "Spot"
  },
  "T": {
   "type": "number",
   "description": "Years to expiry"
  },
  "r": {
   "type": "number",
   "description": "Risk-free rate"
  },
  "type": {
   "type": "string",
   "description": "call | put"
  },
  "sigma": {
   "type": "number",
   "description": "Volatility"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "type": "call",
  "price": 10.45058357218556,
  "greeks": {
   "delta": 0.6368306511756191,
   "gamma": 0.0187620173458469
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/agent402-uk-black-scholes-options-pricer-123f6531/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from agent402.co.uk](https://www.zero.xyz/host/agent402.co.uk/llms.txt)