What a greek measures
A greek measures how a model option price responds to one input, holding the other inputs fixed. Delta measures sensitivity to the underlying forward; gamma measures how delta changes; vega measures sensitivity to implied volatility (IV); theta measures sensitivity to passing time. These are local estimates for small changes, not realised profit or loss. Long-option sensitivities below reverse sign for a short position.
The model the chain uses
The BTC options chain computes gamma, vega and theta with Black-76 on the forward, r = 0. F is the venue's forward in USD, K is the strike, σ is that leg's annualised mark IV as a decimal (50% means 0.50), and T is remaining years. The forward is the expiry-specific underlying reference for this futures-style option model; substituting today's spot price can change the greeks.
T = (expiry_ms − now_ms) / (365 × 86,400,000). The model uses fractional calendar days and a 365-day year, not trading days. Its common input is d1 = (ln(F / K) + σ² T / 2) / (σ √T). N is the standard normal cumulative distribution function; φ is its density. The formulas require positive F, K, σ and T; expired or missing inputs do not produce a valid estimate.
Illustrative: not live data. Every example below uses F = $100,000, K = $100,000, σ = 50% and T = 30/365, per 1 coin of underlying. Gamma, vega and theta are identical for calls and puts at these same inputs under r = 0. Actual contract sizes and settlement currencies can differ; these chain units are not a per-contract cash payout.
Delta: sensitivity to the forward
delta_call = N(d1); delta_put = N(d1) − 1. This is plain, not premium-adjusted delta: it does not subtract an adjustment for the option premium. Delta is dimensionless, the model USD price change per $1 forward move per 1 coin. The example call delta is 0.529 and put delta is −0.471. A small $1 rise in F therefore adds about $0.529 to the call's model value and subtracts about $0.471 from the put's, with other inputs fixed.
The chain displays the venue's delta; the site's 25-delta IV calculations prefer venue delta and fall back to this Black-76 delta when needed. A +0.25 call or −0.25 put is a sensitivity target, not a probability guarantee or a promise about expiry.
Gamma: how delta changes
gamma = φ(d1) / (F σ √T). The chain's Gamma (per $1) is the change in delta per $1 move of the forward. In the example it is 0.00002776 per $1: a small $1 rise increases either long option's delta by about 0.00002776. Gamma is positive for both long calls and long puts. It tends to be highest near the money and grows near expiry for near-the-money options; far-out-of-the-money gamma need not grow. Read gamma exposure for aggregation across open interest and its sign assumptions.
Vega: sensitivity to IV
vega = F φ(d1) √T / 100. The chain's Vega (USD) is per 1 vol point, an absolute 0.01 change in decimal IV, per 1 coin. Moving IV from 50% to 51% is one vol point, not a 1% relative rise. Example vega is $114.08: that one-point increase adds about $114.08 to either long option's model value with other inputs fixed. It is not the sensitivity to an increase of 1.00 in decimal IV.
Theta: passing calendar time
theta = −F φ(d1) σ / (2 √T) / 365. The chain's Theta (USD/day) is per calendar day, per 1 coin. Example theta is −$95.07 per day, so one day passing reduces either long option's model value by about $95.07 with F and IV held fixed. It is an instantaneous daily rate, not exact one-day repricing or a fixed daily loss: theta itself changes as expiry approaches, and price and IV also move.
Model vs venue greeks
The chain labels gamma, vega and theta model because they are our estimates from each leg's mark IV and the venue's forward, with time to expiry counted from now. Delta comes from the venue. The model greeks are not venue quotes; missing mark IV or forward leaves a dash. A venue can publish greeks computed with another timestamp, IV, forward or interest rate. Plain and premium-adjusted delta conventions can also differ between products. Compare inputs, units and conventions before comparing numbers.
Black-76 is an idealised model. Volatility smiles, changing IV, liquidity, fees, funding, settlement rules and discrete hedges limit these fixed-input estimates. Greeks do not establish executable prices or a profitable strategy. This guide is educational and not trading advice.
Primary model and exchange references checked on 17 October 2026: Black (1976): The pricing of commodity contracts · Bybit: option ticker greek fields · Deribit: ticker greeks. Not financial advice.