What model does this use?

It uses the classic Black-Scholes-Merton model for European vanilla options on a non-dividend-paying asset. Crypto perpetual and dated options on Deribit and Lyra are European-style, so Black-Scholes is the standard pricing and Greeks framework, with implied volatility as the key input.

How is delta interpreted?

Delta is the change in option price for a $1 change in the spot. A call delta runs from 0 to 1, a put delta from −1 to 0. A delta of 0.5 means the option gains about $0.50 for every $1 the spot rises. Delta also approximates the probability the option expires in the money.

What are theta and vega in these units?

Theta here is the value lost per calendar day as expiry approaches (it is the annual theta divided by 365). Vega is the price change for a 1 percentage-point move in implied volatility. Both are shown per the conventions traders use day to day.

Why do my Greeks differ from the exchange's?

Exchanges may use a slightly different rate, a volatility surface rather than a single IV, or include funding and dividends. This tool uses a single flat IV and rate, which is the textbook Black-Scholes case — close, but not identical to a venue's live risk engine.

Is any data sent to a server?

No. The pricing and Greeks are computed entirely in your browser using a numerical normal distribution. None of your inputs leave your device.

Crypto Options Greeks Calculator (Black-Scholes)

The Crypto Options Greeks Calculator prices a European vanilla option with the Black-Scholes-Merton model and returns all five Greeks for both a call and a put. It is built for traders on Deribit, Lyra, and similar venues who need fast, accurate sensitivities from spot, strike, time, implied volatility, and rate.

How it works

Black-Scholes defines two intermediate terms from your inputs (S = spot, K = strike, T = years to expiry, σ = implied volatility, r = risk-free rate):

d1 = ( ln(S/K) + (r + σ²/2)·T ) / ( σ·√T )
d2 = d1 − σ·√T

The prices are then:

Call = S·N(d1) − K·e^(−rT)·N(d2)
Put  = K·e^(−rT)·N(−d2) − S·N(−d1)

where N is the standard normal cumulative distribution. The calculator evaluates N with a high-accuracy numerical approximation. The Greeks follow directly:

Delta: N(d1) for a call, N(d1) − 1 for a put
Gamma: N′(d1) / (S·σ·√T) — shared by call and put
Vega: S·N′(d1)·√T (shown per 1% IV move)
Theta: the time-decay term (shown per calendar day)
Rho: K·T·e^(−rT)·N(d2) for a call

Example and notes

A BTC call with spot $60,000, strike $60,000, 30 days to expiry, 70% IV, and a 4% rate prices near the money with a delta close to 0.55 and a large gamma and vega because it is at the money with meaningful time left. As expiry approaches, theta accelerates and gamma concentrates around the strike.

The model assumes a single flat implied volatility and rate. A live exchange risk engine uses a full volatility surface and may include funding, so treat these as the textbook reference values rather than an exact match to a venue quote.