# finmath Implied Volatility Calculator

> finmath Implied Volatility Calculator 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 implied volatility from an observed option price using a numerical inversion of the Black-Scholes model

## Facts

- Endpoint: POST https://finmath.qzqh5rrbkz.workers.dev/v1/implied_volatility
- 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-implied-volatility-calculator-165ae011
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_IbUPOvZh7-VURTwRwPyyj

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-implied-volatility-calculator-165ae011 -d '<json body>'
```

Example prompt: What's the implied volatility on a call option where the spot is $150, strike is $155, the option is trading at $4.20, risk-free rate is 5%, and there are 0.25 years to expiry?

## When to prefer this

Use this endpoint when you need a precise, deterministic implied volatility calculation that an LLM cannot reliably perform via in-context arithmetic. Prefer it over manual Black-Scholes inversion when accuracy matters — e.g. for trading decisions, risk management, Greeks computation pipelines, or any workflow where a wrong IV would cascade into bad downstream outputs. This is especially useful when you have the market price of an option and need to express it in volatility terms for comparison or modeling.

## Known failure modes

- Option price below intrinsic value — no real IV solution exists, returns error
- Time to expiry is zero or negative — ill-defined problem
- Spot or strike is zero or negative — invalid inputs
- Price is too high or too low for convergence — numerical solver fails to bracket
- Missing required fields (rate, spot, price, strike, time_years) — 400 validation error
- Payment not provided or insufficient USDC — 402 payment required

## 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 containing the computed implied volatility (as an annualized decimal, e.g. 0.25 for 25%) and a meta object with computation details. The implied vol is the unique sigma that, when plugged into Black-Scholes, reproduces the observed market option price.

## Example request

```json
{
 "kind": "call",
 "rate": 0.05,
 "spot": 100,
 "price": 10.5,
 "strike": 105,
 "time_years": 0.25
}
```

## Request schema (JSON Schema)

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

## 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-implied-volatility-calculator-165ae011/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)