# finmath Black-Scholes Option Pricer

> finmath Black-Scholes Option Pricer is a paid API for AI agents from finmath.qzqh5rrbkz.workers.dev, paid per call via x402, $0.003/call, status unknown (last checked 2026-09-15).

Computes Black-Scholes option price and Greeks for a European call or put given spot, strike, rate, volatility, and time to expiry

## Facts

- Endpoint: POST https://finmath.qzqh5rrbkz.workers.dev/v1/black_scholes_option
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/finmath-black-scholes-option-pricer-11fa05d1
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_MOBeWMVydiACcSsf6KbiM

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 finmath-black-scholes-option-pricer-11fa05d1 -d '<json body>'
```

Example prompt: What's the Black-Scholes price and Greeks for a call option on a stock trading at $150, strike $155, risk-free rate 5%, volatility 25%, expiring in 0.5 years?

## When to prefer this

Use this endpoint when you need exact, deterministic Black-Scholes pricing and Greeks rather than relying on an LLM's approximate arithmetic. Prefer it over general-purpose math tools when the task is specifically European option pricing with standard inputs and you need trustworthy numerical output for trading, risk, or educational purposes.

## Known failure modes

- Missing required fields (rate, spot, strike, time_years, volatility) returns a 400-level error
- Negative time_years or volatility may produce undefined/error result
- Invalid option kind string may default to call or return an error
- Payment not included or rejected returns HTTP 402

## How this service works

Deterministic finance and crypto math for AI agents: TradFi (NPV, IRR, XIRR, Black-Scholes + Greeks, bonds, VaR, Sharpe) and DeFi (impermanent loss, perp liquidation, funding, Uniswap v3, health factor, cost basis). Exact, model-free arithmetic that LLMs get wrong — priced per call in USDC.

## Output

Returns a result object with the computed option price and associated Greeks (delta, gamma, theta, vega, rho), plus a meta object with call metadata. Values are exact arithmetic outputs, not LLM estimates.

## Example request

```json
{
 "kind": "call",
 "rate": 0.05,
 "spot": 100,
 "strike": 100,
 "time_years": 1,
 "volatility": 0.2
}
```

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "rate",
  "spot",
  "strike",
  "time_years",
  "volatility"
 ],
 "properties": {
  "kind": {
   "type": "string",
   "description": "kind"
  },
  "rate": {
   "type": "number",
   "description": "rate"
  },
  "spot": {
   "type": "number",
   "description": "spot"
  },
  "strike": {
   "type": "number",
   "description": "strike"
  },
  "time_years": {
   "type": "number",
   "description": "time_years"
  },
  "volatility": {
   "type": "number",
   "description": "volatility"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "result",
  "meta"
 ],
 "properties": {
  "meta": {
   "type": "object"
  },
  "result": {}
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/finmath-black-scholes-option-pricer-11fa05d1/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from finmath.qzqh5rrbkz.workers.dev](https://www.zero.xyz/host/finmath.qzqh5rrbkz.workers.dev/llms.txt)