The Greeks: Five Sensitivities, Not Five Predictions

That framing matters because the Greeks are frequently presented as a trading toolkit, as though knowing delta told you what to do. It does not. Knowing delta tells you what your position is currently exposed to, which is genuinely valuable and entirely different. This article defines the five, explains what each is useful for, and then spends real space on their limitations — because a set of numbers that changes continuously, is computed from a model whose assumptions are known to be imperfect, and is valid only for small moves is a set of numbers that invites more confidence than it can support.

The five

Delta measures sensitivity to the price of the underlying: how much the option's value changes for a one-unit move in the underlying. Calls have positive delta (0 to 1), puts negative (−1 to 0). A call with delta 0.45 gains roughly $0.45 per $1 rise in the underlying — so on a 100-share contract, about $45. Two further uses. Delta is often read as a rough proxy for the probability of finishing in the money, which is a serviceable intuition and not literally the same quantity — a distinction worth keeping. And delta aggregates: a portfolio's net delta expresses its total directional exposure in underlying-equivalent terms, which is the single most useful thing the Greeks do. Gamma measures sensitivity of delta to the underlying — the rate at which your directional exposure itself changes. High gamma means delta moves quickly, so a position that looked modestly exposed can become heavily exposed after a move you did not act on. Gamma is largest at the money and rises sharply as expiry approaches, which is the mathematical core of why very short-dated options behave violently and why the 0DTE article exists. Theta measures sensitivity to the passage of time — the decay the previous article established as certain arithmetic. Theta is negative for option buyers (value bleeds away) and positive for writers, quoted per day, and it accelerates toward expiry. A theta of −0.04 means roughly four cents of value lost per day per unit, other things equal — and "other things equal" is doing a great deal of work, since the underlying rarely sits still. Vega measures sensitivity to implied volatility: how much the option's value changes for a one-percentage-point change in the volatility the market is pricing. Vega is positive for buyers of both calls and puts, because more expected movement makes an option more valuable regardless of direction. This is the Greek that surprises people most: an option can lose value while the underlying moves favourably, if implied volatility falls enough at the same time — the phenomenon informally called volatility crush, common after an earnings announcement resolves the uncertainty that was being priced. The implied-volatility article takes this up. Rho measures sensitivity to interest rates, and is the least consequential for most retail-relevant positions and short maturities — though it becomes material for long-dated contracts and in periods of significant rate movement, so treating it as negligible is a convention rather than a rule.

What they are for, and what they cannot do

The legitimate uses are real. Greeks let a holder state their exposure precisely rather than approximately: not "I own some calls" but "this position gains about $45 per $1 of underlying movement, loses about $12 a day to decay, and gains about $30 per point of implied volatility." They let exposures across multiple positions be aggregated, which is the only practical way to know what a book of options actually does. And they make risks visible that are otherwise easy to ignore — most importantly theta, since a position bleeding value while nothing appears to happen is the commonest unpleasant surprise in options. Now the limitations, and there are five. They are instantaneous. Every Greek describes the sensitivity right now, at this price, on this date, at this implied volatility. Move any of those and all of them change — which is what gamma is, and gamma itself changes too. A Greek is a photograph, not a trajectory. They assume small moves. The linear approximation delta provides is reasonable for a 1% move and unreliable for a 15% one, precisely when it matters most. Gamma partially corrects this, and the correction is itself an approximation. They are model outputs. Greeks are computed, not observed — they come out of a pricing model with assumptions about the distribution of returns, and those assumptions are known to understate extreme moves. Two providers may publish slightly different Greeks for the same contract because they used different inputs or models. They change together. Real markets do not move one variable at a time: a sharp fall in the underlying typically arrives with a rise in implied volatility, so delta and vega effects combine in ways no single Greek captures. And they say nothing about direction. Delta tells you your exposure to a move; it does not tell you whether the move will happen. This is the misuse this article most wants to prevent: the Greeks are a description of a position, not a forecast about a market, and no configuration of them makes a position advisable. They are worth understanding because a reader who cannot state their delta and theta does not know what they hold. They are not worth mistaking for insight into what happens next.