# Hermes Plant Black-Scholes Option Pricing & Greeks

> Hermes Plant Black-Scholes Option Pricing & Greeks is a paid API for AI agents from hermesplant.com, paid per call via x402, $0.25/call, status unknown (last checked 2026-09-15).

Computes Black-Scholes-Merton option price along with full Greeks (delta, gamma, theta, vega, rho) for a given options contract, paid per call via x402.

## Facts

- Endpoint: GET https://hermesplant.com/api/agent-services/options/price
- Price: $0.25/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/hermes-plant-black-scholes-option-pricing-greeks-c55587f6
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_jGXeaXxzgIY9sDJS-W8Pc

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 hermes-plant-black-scholes-option-pricing-greeks-c55587f6
```

Example prompt: Price a European call option where the underlying is at $100, strike is $100, time to expiration is 1 year, risk-free rate is 5%, and implied volatility is 20% — give me the full Greeks including delta, gamma, theta, vega, and rho.

## When to prefer this

Choose this endpoint when an AI agent needs fast, deterministic, test-backed Black-Scholes option pricing with a full Greeks output in a single call, especially in autonomous trading or risk workflows that require pay-per-call metering via x402. Prefer over in-house implementations when auditability, structured findings output, and deterministic test-backed results matter.

## Known failure modes

- Missing required input parameters (underlying price, strike, expiry, volatility, rate) returns a 4xx validation error
- Negative or zero volatility input may cause mathematical errors or rejection
- Extremely short time-to-expiry values may produce degenerate Greeks
- Insufficient USDC balance or failed x402 payment returns a payment-required error
- Network timeout if the service is temporarily unavailable

## How this service works

Deterministic Black-Scholes-Merton European option pricing and Greeks. Returns price, d1/d2, full Greeks (delta, gamma, vega, theta, rho) in canonical and conventional display units (vega per 1%, theta per day, rho per 1%), plus intrinsic value, time value, and moneyness. Supports continuous dividend yield. Pure math from caller-supplied parameters — no market-data feed, no fabrication.

## Output

Returns the theoretical option price, d1 and d2 intermediate values, moneyness classification (at-the-money/in-the-money/out-of-the-money), intrinsic value, time value, and a complete Greeks bundle (delta, gamma, theta, vega, rho, plus per-1% and per-day convenience scalings), along with a valuation findings summary and a unique requestId.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "spot": {
   "type": "number",
   "description": "Current price of the underlying (> 0)."
  },
  "strike": {
   "type": "number",
   "description": "Option strike price (> 0)."
  },
  "optionType": {
   "type": "string",
   "description": "'call' or 'put' (default 'call')."
  },
  "volatility": {
   "type": "number",
   "description": "Annualized volatility (sigma) as a fraction, e.g. 0.2 for 20%."
  },
  "riskFreeRate": {
   "type": "number",
   "description": "Annual continuously-compounded risk-free rate, e.g. 0.05 (default 0)."
  },
  "timeToExpiry": {
   "type": "number",
   "description": "Time to expiry in years (e.g. 0.5 = 6 months)."
  },
  "dividendYield": {
   "type": "number",
   "description": "Annual continuous dividend yield, e.g. 0.02 (default 0)."
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "d1": 0.35,
  "d2": 0.15,
  "price": 10.450576,
  "greeks": {
   "rho": 53.232483,
   "vega": 37.524035,
   "delta": 0.636831,
   "gamma": 0.018762,
   "theta": -6.414028,
   "rhoPer1Pct": 0.532325,
   "thetaPerDay": -0.017573,
   "vegaPer1Pct": 0.37524
  },
  "service": "optionlens",
  "findings": [
   {
    "fix": null,
    "why": "Black-Scholes-Merton valuation summary.",
    "rule": "valuation",
    "evidence": "price=10.4506 d1=0.35 d2=0.15 moneyness=at-the-money",
    "severity": "info"
   }
  ],
  "moneyness": "at-the-money",
  "requestId": "opt-db556a1a",
  "timeValue": 10.450576,
  "optionType": "call",
  "intrinsicValue": 0
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/hermes-plant-black-scholes-option-pricing-greeks-c55587f6/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from hermesplant.com](https://www.zero.xyz/host/hermesplant.com/llms.txt)