# Black-Scholes Greeks Lite

> Black-Scholes Greeks Lite is a paid API for AI agents from api.delx.ai, paid per call via x402, $0.001/call, status unknown (last checked 2026-09-15).

Computes a compact set of Black-Scholes Greeks (delta, gamma, vega, theta) for a European call option using deterministic local math

## Facts

- Endpoint: POST https://api.delx.ai/api/v1/x402/bs-greeks-lite
- Price: $0.001/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/black-scholes-greeks-lite-5116cbd4
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_ekBBrIidCt2kuqa9c5fDQ

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 black-scholes-greeks-lite-5116cbd4 -d '<json body>'
```

Example prompt: Calculate the Black-Scholes Greeks for a European call with spot price 105, strike 100, annualized vol of 20%, 0.5 years to expiry, and a risk-free rate of 5% — I need delta, gamma, vega, and theta in one compact result.

## When to prefer this

Choose this endpoint when you need a fast, offline, deterministic Black-Scholes Greeks calculation for a European call with no dependency on live market data, API keys, or external pricing feeds. It is ideal for risk reporting pipelines, hedging ratio calculations, or any agent workflow that needs a compact delta/gamma/vega/theta pack at minimal cost ($0.001 USDC). Prefer the full Black-Scholes Delta endpoint if you need only delta with put support. Use this lite endpoint when you need all four Greeks in a single call without overhead.

## Known failure modes

- Missing required fields (spot, strike, vol, t_years) returns a validation error
- vol <= 0 or t_years <= 0 causes undefined or error response since these must be strictly positive
- Extremely short expiry or deep out-of-the-money inputs may produce near-zero Greeks that appear incorrect but are mathematically valid
- Payment failure via x402 will prevent the call from being processed
- Passing non-numeric types for numeric fields will cause schema validation failure

## How this service works

Delta/gamma/vega/theta lite for European call (BS). Call when risk report needs a compact Greeks pack offline. Returns delta, gamma, vega, theta_call as deterministic JSON for $0.001 USDC via x402 on Base. First-party local math only—no RPC, live market feed, API keys, storage, or mediagen. Advisory only; the caller owns capital, risk, and production controls.

## Output

Returns a deterministic JSON object containing four Greek values for the European call: delta (price sensitivity to spot), gamma (rate of change of delta), vega (sensitivity to volatility), and theta_call (time decay per day or year as defined). All values are computed via closed-form Black-Scholes math with no external dependencies.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "vol": {
   "type": "number",
   "description": "Annualized volatility as decimal (>0), e.g. 0.2 = 20%"
  },
  "rate": {
   "type": "number",
   "description": "Risk-free rate as decimal (optional, default 0)"
  },
  "spot": {
   "type": "number",
   "description": "Underlying spot price (>0)"
  },
  "strike": {
   "type": "number",
   "description": "Option strike price (>0)"
  },
  "t_years": {
   "type": "number",
   "description": "Time to expiry in years (>0)"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "vega": 0.199221957047382,
  "delta": 0.5199388058383725,
  "gamma": 0.0398443914094764,
  "schema": "delx/util-bs-greeks-lite/v1",
  "theta_call": -0.02183254323806927
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/black-scholes-greeks-lite-5116cbd4/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from api.delx.ai](https://www.zero.xyz/host/api.delx.ai/llms.txt)