# Delx Commerce — Black-Scholes Delta Calculator

> Delx Commerce — Black-Scholes Delta 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 delta (call and put) for an option given spot, strike, volatility, time to expiry, and risk-free rate

## Facts

- Endpoint: POST https://commerce.delx.ai/api/v1/x402/bs-delta?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-commerce-black-scholes-delta-calculator-a2fb7628
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_5qlDl2mfn8Xa-fcH1AKXp

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-commerce-black-scholes-delta-calculator-a2fb7628 -d '<json body>'
```

Example prompt: What's the call and put delta for an 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%?

## When to prefer this

Choose this endpoint when you need a fast, pay-per-call Black-Scholes delta computation without API key signup, especially in agentic workflows where micropayments via USDC (x402 protocol) are acceptable. Ideal for one-off or low-volume options greek calculations where subscribing to a full financial data service is overkill.

## Known failure modes

- Missing required fields (spot, strike, vol, t_years) returns a validation error
- vol <= 0 or spot <= 0 or strike <= 0 causes invalid input error
- t_years <= 0 (expired option) causes invalid input error
- Payment failure via x402 if USDC balance is insufficient or transaction is rejected

## 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 with schema identifier 'delx/util-bs-delta/v1', containing delta_call (positive float between 0 and 1 representing call option delta) and delta_put (negative float between -1 and 0 representing put option delta), computed using the Black-Scholes model.

## 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": {
  "schema": "delx/util-bs-delta/v1",
  "delta_put": -0.4800611941616275,
  "delta_call": 0.5199388058383725
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/delx-commerce-black-scholes-delta-calculator-a2fb7628/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)