# Black-Scholes d1 d2 Calculator

> Black-Scholes d1 d2 Calculator 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 Black-Scholes d1 and d2 intermediate values from spot price, strike price, volatility, time to expiry, and risk-free rate

## Facts

- Endpoint: POST https://api.delx.ai/api/v1/x402/bs-d1-d2
- 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-d1-d2-calculator-501570d2
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap__QxijYNmZcjD0kXjNYix5

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-d1-d2-calculator-501570d2 -d '<json body>'
```

Example prompt: Calculate Black-Scholes d1 and d2 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 deterministic, purely local Black-Scholes d1 and d2 values with no dependency on live market data, API keys, or external feeds. Ideal for options Greeks pipelines that supply their own spot/vol/rate inputs and need a reliable, cheap, stateless math primitive. Prefer over rolling your own implementation when you want a verified, auditable result at $0.001 USDC per call.

## Known failure modes

- Invalid input: spot or strike <= 0 returns error
- Invalid input: vol <= 0 returns error
- Invalid input: t_years <= 0 returns error
- Missing required fields returns validation error
- Payment failure: insufficient USDC balance or x402 protocol error

## How this service works

Compute Black-Scholes d1 and d2 from spot/strike/vol/time/rate. Call when you need BS inputs for Greeks without a market feed. Returns d1 and d2 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 the computed d1 and d2 scalar values derived from the Black-Scholes formula, given the provided spot price, strike price, volatility, time to expiry, and risk-free rate. No market data is fetched; computation is purely local math.

## 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": {
  "d1": 0.05000000000000001,
  "d2": -0.05,
  "schema": "delx/util-bs-d1-d2/v1"
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/black-scholes-d1-d2-calculator-501570d2/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)