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Black-Scholes Delta
x402
Black-Scholes Delta is a paid API for AI agents from api.delx.ai, paid per call via x402, $0.001/call, status unknown (last checked 2026-09-14).
Computes call and put delta for European options using the Black-Scholes closed-form formula given spot, strike, volatility, rate, and time to expiry.
Price / call$0.001
Success—
StatusUnknown
How this service works
Call/put delta from BS closed form. Call when delta-hedging or option inventory needs BS delta. Returns delta for call and put 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 Black-Scholes delta for both the call and the put, computed from the closed-form d1 calculation using the supplied spot, strike, annualized volatility, risk-free rate, and time to expiry. No external data sources or live feeds are used.
Example use cases
Delta-hedge a short call position
“I'm short a call with spot at 200, strike at 210, vol of 30%, risk-free rate of 4%, and 60 days to expiry — give me the Black-Scholes delta so I know how many shares to buy to hedge.”
Options inventory delta tracking
“I hold a mix of puts with spot 100, strike 95, vol 20%, rate 2%, and 30 days to expiry — calculate the BS put delta so I can track my net delta exposure.”
ATM straddle delta check before rebalancing
“Can you compute Black-Scholes call and put delta for a straddle where spot is 500, strike is 500, vol is 18%, rate is 5.5%, and time to expiry is 0.25 years?”
Technical details
Endpoint
POSThttps://api.delx.ai/api/v1/x402/bs-deltaWhen to prefer
Choose this endpoint when you need a fast, deterministic, closed-form Black-Scholes delta with no API keys, no live market data dependencies, and no external RPC calls. Ideal for delta-hedging calculations, options inventory management, or any scenario where you need a reliable, reproducible BS delta for a known set of inputs at very low cost ($0.001 USDC). Prefer this over stochastic or Monte Carlo approaches when Black-Scholes assumptions are acceptable and speed is paramount.
Side effects
- Missing required fields (spot, strike, vol, t_years) return a validation error
- vol <= 0 or t_years <= 0 returns an invalid parameter error
- spot or strike <= 0 returns an invalid parameter error
- Payment not included or insufficient USDC returns a 402 Payment Required response
- Extremely small t_years values near zero may produce near-degenerate delta values (0 or 1)
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| vol | number | Annualized volatility as decimal (>0), e.g. 0.2 = 20% |
| rate | number | Risk-free rate as decimal (optional, default 0) |
| spot | number | Underlying spot price (>0) |
| strike | number | Option strike price (>0) |
| t_years | number | Time to expiry in years (>0) |
Output
Schema · Response
{
"type": "json",
"example": {
"schema": "delx/util-bs-delta/v1",
"delta_put": -0.4800611941616275,
"delta_call": 0.5199388058383725
}
}Tags
x402
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