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Black-Scholes European Option Calculator
x402
Black-Scholes European Option Calculator is a paid API for AI agents from payai.agentstools.dev, paid per call via x402, $0.003/call, status unknown (last checked 2026-10-12).
Computes Black-Scholes fair price, all Greeks (delta, gamma, vega, theta, rho), or implied volatility for European options given spot price, strike, time to expiry, rate, and volatility.
Price / call$0.003
Success—
StatusUnknown
How this service works
Black-Scholes European option calculator: fair price, all greeks (delta, gamma, vega, theta, rho), or implied volatility from a market price. Pure computation over your inputs.
Output
Returns the Black-Scholes fair price and/or Greeks (delta, gamma, vega, theta, rho) for a European option, or the implied volatility solved from an observed market price, depending on the 'op' parameter chosen (price, greeks, or iv).
Example use cases
Hedge delta exposure across option positions
“I'm holding several European call and put options on the same stock. Can you run Black-Scholes calculations for each one — spot at $120, strikes ranging from $110 to $130, 3 months to expiry, 4% rate, and 25% volatility — so I can see which positions have the highest delta and need rehedging?”
Evaluate relative value of traded options
“I just saw a European put option trading at $8.50 in the market — the underlying is at $95, strike is $100, expires in 6 months, risk-free rate is 3.5%, and I estimate volatility at 22%. What's the implied volatility from that market price so I can tell if it's overpriced or underpriced?”
Assess interest rate sensitivity of options
“I want to understand how sensitive my European call option positions are to changes in rates. Can you compute theta, vega, and especially rho for me using Black-Scholes? Spot at $200, strike at $210, 1 year to expiry, 2.5% rate, and 18% volatility — I need to know the rho value most.”
Technical details
Endpoint
GEThttps://payai.agentstools.dev/quant/options?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need fast, pure-compute Black-Scholes analytics for European options — fair pricing, Greeks, or implied volatility — without any market data dependencies. Prefer it over general financial APIs when you already have your own inputs and just need the mathematical result.
Side effects
- Missing required parameters (op, S, K, T, r) returns a 400 error
- Sigma not provided when op=price or op=greeks returns an error
- Market_price not provided when op=iv returns an error
- Non-positive values for S, K, or T cause computation errors
- Implied volatility solver may fail to converge for extreme or nonsensical market prices
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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