Model-Dependent Vs Model-Free Greeks

A "Greek" like delta or vega is usually quoted as a single number produced by plugging option inputs into a pricing model, most commonly Black-Scholes. That number is model-dependent: it's the answer to "how would the price change, according to this specific model, if this one input moved a little?" Change the model — say, add stochastic volatility instead of assuming it's constant — and the same option can get a meaningfully different delta or vega for the exact same market price, because the Greek describes a sensitivity inside the model's assumed world, not a directly observed market fact.

Model-free Greeks flip this around: instead of trusting a model's formula, they're extracted directly from a set of observed option prices across strikes, using only the requirement that prices avoid arbitrage. The classic example is model-free implied variance, built from a weighted basket of out-of-the-money option prices across all strikes (the method behind the VIX index), which recovers the market's expected variance over a horizon without assuming any particular volatility process. Because it's built from the whole shape of quoted prices rather than a single model equation, it survives even if the "true" volatility dynamics are nothing like the model a trader might otherwise have picked.

The practical difference matters most when a book is hedged against a Greek computed under one model but the market actually moves according to different dynamics — the hedge ratio was only ever an answer within a model, and if that model is wrong, the hedge can be systematically off even though the number looked precise.