#greeks

Live (15-minute delayed) US equity and index options chains, served from CBOE's public delayed-quotes feed. For any optionable ticker the summary endpoint returns the underlying quote — current price, day change, open/high/low/close, volume, bid/ask and the 30-day implied volatility (IV30) with its change. The expirations endpoint lists every available expiration date with its call and put contract counts. The chain endpoint returns the option contracts themselves: for each strike and expiry it gives the call/put bid, ask, last, implied volatility, open interest, volume and the full greeks — delta, gamma, theta and vega — and can be filtered by expiration date and by call or put. US index options are addressed with an underscore prefix (_SPX, _VIX). This is the single-name equity and index options surface — strikes, expiries, IV and greeks — distinct from the options-pricing calculators, the crypto-options and the FX/rate APIs in the catalogue. Live, no key on the upstream, nothing stored.

api.oanor.com/optionschain-api

Live on-chain options and perpetuals data from Aevo, a leading decentralized derivatives exchange — no key, nothing stored. This is the on-chain options view: the full option chain with strikes, expiries, mark prices, implied volatility and the option greeks, plus live perpetual stats, distinct from the Deribit-based and other derivatives APIs in the catalogue — Aevo is an on-chain options and perps venue. The options endpoint returns the option chain for an asset — calls and puts by strike and expiry, each with mark and index price, implied volatility and the greeks (delta, gamma, theta, vega, rho). The stats endpoint returns the live perpetual statistics for an asset: open interest, index and mark price, the 24h change, funding and 24h volume. The expiries endpoint lists the available option expiries with their strike range so you can navigate the chain. Build options dashboards, volatility surfaces, greeks calculators and derivatives-trading tools on top of real on-chain Aevo data. Options are listed for BTC, ETH and HYPE; filter by type=call|put and expiry=YYYY-MM-DD, and greeks and IV come straight from the venue.

api.oanor.com/aevo-api

Black-Scholes-Merton European option pricing as an API, computed locally and deterministically. The price endpoint computes the fair value of a European call and put from the spot price, strike, annualized risk-free rate, annualized volatility, time to expiry in years and an optional continuous dividend yield, using Call = S·e^(−qT)·N(d1) − K·e^(−rT)·N(d2) and the put-call-parity put, with d1 = [ln(S/K) + (r − q + σ²/2)·T]/(σ√T) and d2 = d1 − σ√T and a high-accuracy standard-normal CDF — an at-the-money option on a 100 spot with a 5 % rate, 20 % volatility and one year to expiry is worth about 10.45 for the call and 5.57 for the put. The greeks endpoint returns the full risk sensitivities for both call and put: delta (∂V/∂S), gamma (∂²V/∂S²), vega (∂V/∂σ, per 1.00 and per 1 % point), theta (∂V/∂t, per year and per calendar day) and rho (∂V/∂r). Rates, dividend yield and volatility are annualized and time is in years, continuous compounding. Everything is computed locally and deterministically, so it is instant and private. Ideal for fintech, trading, quant, portfolio-risk, derivatives and finance-education app developers, option-pricing and Greeks dashboards, and risk engines. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 2 endpoints. This is the European Black-Scholes model; for American-style early exercise or implied volatility solving it returns the closed-form European result only.

api.oanor.com/blackscholes-api

Black-Scholes option-pricing maths as an API, computed locally and deterministically. The black-scholes endpoint prices European call and put options from the spot price, strike, time to expiry, risk-free rate, volatility and an optional dividend yield — Call = S·e^(−qT)·Φ(d1) − K·e^(−rT)·Φ(d2) — returning both prices, the intermediate d1 and d2, and the put-call parity figure. The greeks endpoint computes the full set of option sensitivities for the call and the put: delta, gamma, theta (per year and per day), vega and rho, the quantities traders use to hedge and manage risk. The implied-volatility endpoint inverts the model, solving by bisection for the volatility that reproduces a given option market price. Rates, volatilities and dividend yields are decimals (0.05 = 5 %) and time to expiry is in years. Everything is computed locally and deterministically, so it is instant and private. Ideal for fintech, trading, quantitative-finance and derivatives app developers, options analytics and risk tools, and finance education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is options pricing; for NPV and IRR use an NPV API and for CAGR and real returns an investment API.

api.oanor.com/options-api