Option pricing, Black-Scholes and Greeks
options_pricePrice a European call and put with Black-Scholes-Merton and get delta, gamma, vega (per vol point), theta (per day), rho, d1, d2 and the probability of ending in the money; or give a market price and get the implied volatility. Inputs: spot, strike, expiry date or days, volatility, interest rate and dividend or funding yield in percent. Pure arithmetic, no data source. Use for crypto, stock or FX options, to price a quote or size a hedge. Example: spot=100, strike=100. Price $0.01/call via x402 USDC or a card key (/credits), first 25 free; failed calls free. Reads or computes only and changes nothing; each call is charged, so repeats are not free.
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| vol | No | Annual volatility in percent, e.g. 20 (default 50); not needed with price | |
| days | No | Days to expiry (default 30), or give expiry or years | |
| rate | No | Risk-free rate in percent per year, e.g. 5 for 5% (default 0) | |
| spot | Yes | Price of the underlying | |
| type | No | call or put, for the implied volatility (default call) | |
| price | No | A market option price: returns the implied volatility | |
| years | No | Years to expiry, instead of days | |
| expiry | No | Expiry date (ISO), instead of days | |
| strike | Yes | Strike price | |
| dividend | No | Dividend, funding or borrow yield in percent per year (default 0) |