# Delx BS Greeks Lite — Black-Scholes Options Greeks Calculator

> Delx BS Greeks Lite — Black-Scholes Options Greeks Calculator is a paid API for AI agents from commerce.delx.ai, paid per call via x402, $0.001/call, status unknown (last checked 2026-10-01).

Computes Black-Scholes options Greeks (delta, gamma, theta, vega) for a given option using spot price, strike, volatility, time to expiry, and risk-free rate

## Facts

- Endpoint: POST https://commerce.delx.ai/api/v1/x402/bs-greeks-lite?utm_source=zero.xyz
- Price: $0.001/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-01
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/delx-bs-greeks-lite-black-scholes-options-greeks-calculator-93196a83
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_PayqAdcSEI5O02xfD2ZOh

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 delx-bs-greeks-lite-black-scholes-options-greeks-calculator-93196a83 -d '<json body>'
```

Example prompt: Calculate the Black-Scholes Greeks for a call option with a spot price of 100, strike of 105, annualized volatility of 20%, 0.25 years to expiry, and a risk-free rate of 5% — I need delta, gamma, theta, and vega.

## When to prefer this

Choose this endpoint when you need a fast, pay-per-call, no-signup Black-Scholes Greeks computation with cryptographic payment via USDC on Base or Solana. Ideal for AI agents that need occasional or burst options analytics without committing to a subscription, or when verifiable on-chain payment is required. Best for single-option Greek calculations rather than bulk portfolio analytics.

## Known failure modes

- Missing or zero/negative spot price returns validation error
- Missing or zero/negative strike price returns validation error
- Zero or negative time to expiry (t_years) returns validation error
- Zero or negative volatility (vol) returns validation error
- Payment failure via x402 protocol results in 402 Payment Required response
- Malformed JSON body returns 400 Bad Request

## How this service works

Pay-per-result APIs for agents. No signup. Exact price. Verifiable delivery. USDC on Base + Solana via x402.

## Output

Returns a JSON object containing Black-Scholes Greeks: delta (rate of change of option price with respect to spot), gamma (rate of change of delta with respect to spot), vega (sensitivity to volatility), and theta_call (time decay of the call option per year), along with a schema identifier string.

## 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/delx-bs-greeks-lite-black-scholes-options-greeks-calculator-93196a83/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from commerce.delx.ai](https://www.zero.xyz/host/commerce.delx.ai/llms.txt)