# Derivatives Pricer — Implied Volatility (Single Premium)

> Derivatives Pricer — Implied Volatility (Single Premium) is a paid API for AI agents from derivatives-pricer-production.up.railway.app, paid per call via x402, $0.03/call, status unknown (last checked 2026-10-11).

Computes implied volatility from an observed option premium using Black-Scholes, returning IV, converged model price, price error, and full analytic Greeks.

## Facts

- Endpoint: POST https://derivatives-pricer-production.up.railway.app/v1/option/implied-vol?utm_source=zero.xyz
- Price: $0.03/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-11
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/derivatives-pricer-implied-volatility-single-premium-660ad0da
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_0bSMHyDAVrFERy8WxpVGn

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 derivatives-pricer-implied-volatility-single-premium-660ad0da -d '<json body>'
```

Example prompt: What's the implied volatility on a European call with underlying at 105, strike 100, premium of 8.50, 6 months to expiry, risk-free rate 5%, and no dividends? Also give me the full Greeks.

## When to prefer this

Choose this endpoint when you need to invert an observed market premium to its implied volatility under Black-Scholes for a European option, especially when you also need analytic Greeks in the same call. Prefer it over a full options chain or surface endpoint when you have a single premium observation. Because it requires no API keys and charges a flat $0.03 USDC per call via x402, it is ideal for agent workflows needing on-demand, pay-per-use IV computation without credential management.

## Known failure modes

- Non-convergence: if the premium is outside the no-arbitrage bounds or the solver cannot converge within its iteration limit, 'converged' will be false and impliedVol may be null or unreliable
- Invalid inputs: strike or underlying <= 0 returns a 400-level validation error
- Negative premium or premium exceeding intrinsic value causes solver divergence
- Very short or zero timeToExpiry can cause numerical instability in vega and thus IV solver failure
- Payment failure: if the x402 USDC micropayment on Solana or Base is not completed, the request is rejected with a 402 Payment Required

## How this service works

x402-paid Black-Scholes European option pricing, Greeks, IV surfaces, price/scenario on submitted smiles (TV bilinear), portfolio risk, free demo, and MCP. USDC exact on Solana (PayAI) and/or Base (CDP when configured). Receive wallets appear only in HTTP 402, never on free discovery.

## Output

Returns a JSON object with the computed implied volatility (as a decimal, e.g. 0.20 = 20%), whether the Newton-Raphson solver converged, the number of iterations taken, the Black-Scholes model price at that IV, the price error versus the input premium, the five analytic Greeks (delta, gamma, theta, vega, rho), a mirror of the original inputs, a requestId, and a timestamp.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "rate": {
   "type": "number",
   "description": "Continuous risk-free rate r"
  },
  "strike": {
   "type": "number",
   "description": "Strike K (> 0)",
   "exclusiveMinimum": 0
  },
  "premium": {
   "type": "number",
   "minimum": 0,
   "description": "Observed market premium"
  },
  "treeSteps": {
   "type": "integer",
   "maximum": 500,
   "minimum": 50
  },
  "expiration": {
   "type": "string",
   "format": "date-time"
  },
  "optionType": {
   "enum": [
    "call",
    "put"
   ],
   "type": "string"
  },
  "underlying": {
   "type": "number",
   "description": "Underlying price S (> 0)",
   "exclusiveMinimum": 0
  },
  "optionStyle": {
   "enum": [
    "european",
    "american"
   ],
   "type": "string",
   "default": "european"
  },
  "forwardStart": {
   "type": "string",
   "format": "date-time"
  },
  "timeToExpiry": {
   "type": "number",
   "minimum": 0,
   "description": "Time to expiry in years (xor expiration)"
  },
  "dividendYield": {
   "type": "number",
   "minimum": 0,
   "description": "Continuous yield q (default 0)"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "model": "black-scholes-merton",
  "greeks": {
   "rho": 53.23248343,
   "vega": 37.52403469,
   "delta": 0.63683059,
   "gamma": 0.01876202,
   "theta": -6.41402764
  },
  "inputs": {
   "rate": 0.05,
   "strike": 100,
   "premium": 10.45057562,
   "optionType": "call",
   "underlying": 100,
   "optionStyle": "european",
   "timeToExpiry": 1,
   "dividendYield": 0
  },
  "converged": true,
  "requestId": "00000000-0000-4000-8000-000000000003",
  "computedAt": "2026-01-01T00:00:00.000Z",
  "impliedVol": 0.2,
  "iterations": 12,
  "modelPrice": 10.45057562,
  "priceError": 0,
  "optionStyle": "european",
  "greeksQuality": "analytic"
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/derivatives-pricer-implied-volatility-single-premium-660ad0da/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from derivatives-pricer-production.up.railway.app](https://www.zero.xyz/host/derivatives-pricer-production.up.railway.app/llms.txt)