# QuantOracle Lookback Option Pricer

> QuantOracle Lookback Option Pricer is a paid API for AI agents from api.quantoracle.dev, paid per call via x402, $0.008/call, status unknown (last checked 2026-09-14).

Prices floating or fixed lookback options using the underlying asset price, historical minimum/maximum, volatility, and time parameters

## Facts

- Endpoint: POST https://api.quantoracle.dev/v1/derivatives/lookback-option
- Price: $0.008/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/api-quantoracle-dev-f8b937b6
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_nTA5n6l_AaSN7YVeTcBFg

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 api-quantoracle-dev-f8b937b6 -d '<json body>'
```

Example prompt: Price a floating lookback call option where the current stock price is $100, the historical minimum is $92, volatility is 25%, risk-free rate is 5%, no dividends, and 6 months to expiration.

## When to prefer this

Use this endpoint when you need to price exotic path-dependent lookback options (floating or fixed strike) analytically. Prefer this over vanilla Black-Scholes endpoints when the payoff depends on the historical minimum or maximum of the asset price over the option's life.

## Known failure modes

- Missing required fields (S, T, sigma, type) returns validation error
- Invalid lookback_type value (not 'floating' or 'fixed') returns error
- Negative or zero time-to-expiry (T) causes pricing failure
- sigma of 0 or negative causes numerical instability
- S_min greater than S for a floating call may produce unexpected results
- Payment failure or insufficient USDC balance returns 402

## How this service works

QuantOracle: derivatives/lookback-option

## Output

Returns the theoretical price of the lookback option (e.g. 16.33), the lookback type used (floating or fixed), and the server-side computation time in milliseconds.

## Example request

```json
{
 "S": 100,
 "T": 0.5,
 "q": 0,
 "r": 0.05,
 "type": "call",
 "S_min": 92,
 "sigma": 0.25,
 "lookback_type": "floating"
}
```

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "K": {
   "anyOf": [
    {
     "type": "number"
    },
    {
     "type": "null"
    }
   ],
   "title": "K",
   "description": "Fixed strike price (required for fixed lookback)"
  },
  "S": {
   "type": "number",
   "title": "S",
   "description": "Current spot price",
   "exclusiveMinimum": 0
  },
  "T": {
   "type": "number",
   "title": "T",
   "maximum": 30,
   "description": "Time to expiration in years",
   "exclusiveMinimum": 0
  },
  "q": {
   "type": "number",
   "title": "Q",
   "default": 0,
   "description": "Continuous dividend yield"
  },
  "r": {
   "type": "number",
   "title": "R",
   "default": 0.05,
   "description": "Risk-free interest rate (annualized)"
  },
  "type": {
   "enum": [
    "call",
    "put"
   ],
   "type": "string",
   "title": "Type",
   "default": "call",
   "description": "Option type"
  },
  "S_max": {
   "anyOf": [
    {
     "type": "number"
    },
    {
     "type": "null"
    }
   ],
   "title": "S Max",
   "description": "Maximum price observed so far (for floating put)"
  },
  "S_min": {
   "anyOf": [
    {
     "type": "number"
    },
    {
     "type": "null"
    }
   ],
   "title": "S Min",
   "description": "Minimum price observed so far (for floating call)"
  },
  "sigma": {
   "type": "number",
   "title": "Sigma",
   "description": "Volatility (annualized)",
   "exclusiveMinimum": 0
  },
  "lookback_type": {
   "enum": [
    "floating",
    "fixed"
   ],
   "type": "string",
   "title": "Lookback Type",
   "default": "floating",
   "description": "Floating strike or fixed strike lookback"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/api-quantoracle-dev-f8b937b6/health.json
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