Options Greeks: Delta, Gamma, Theta and Vega

Step 1 of 3 in Options Essentials.

The Greeks are usually taught as partial derivatives, which is accurate and almost useless at the screen. Read as dollars instead, they answer four practical questions: how much do I make if the stock moves a dollar, how fast does that change, what does holding overnight cost me, and what happens if volatility shifts.

Every number below comes from a 30-day at-the-money $100 call, 20% implied volatility, 5% rates — the standard reference position.

The four that matter

The option itself is worth $2.49, or $249 per contract.

Delta: directional exposure, in shares

Delta of 0.540 means the option gains about $0.54 when the stock gains $1 — $54 per contract.

The more useful reading is as share equivalence. A 0.54-delta call behaves like owning 54 shares. Three of them is a 162-share position, and you can compare it directly against a stock position, hedge it, or add it to a portfolio's total exposure.

Calls run 0 to +1, puts 0 to −1. Our 30-day put has a delta of −0.46: it makes $46 per contract when the stock falls a dollar.

Delta is also commonly read as a rough probability of finishing in the money — a 0.54 delta implies roughly a 54% chance. It is an approximation (the precise quantity is a slightly different term in the model), but close enough to be useful when choosing strikes.

Gamma: how fast delta changes

Gamma of 0.069 says that if the stock rises $1, delta goes from 0.540 to about 0.609. Rise another dollar and it climbs again.

That is why long options feel like they accelerate — the position gets longer as it wins and shorter as it loses, automatically. Short options do the reverse, which is the whole risk of selling them: a short call gets shorter into a rally, exactly when you want it to stop.

Gamma is largest at the money and grows sharply as expiry approaches:

Gamma more than triples from 90 days to 7. This is why the final week is where positions go wrong quickly — a small move produces a large change in exposure, and there is no time for it to come back.

Theta: what the clock costs

Theta of −0.045 means the option loses about $4.50 per contract per calendar day, all else equal. Over a weekend, roughly $13.50 — decay runs on calendar days, not trading days.

Look at the table again: theta is $2.88/day at 90 days and $8.58/day at 7. Decay accelerates as expiry nears, and for at-the-money options it is roughly proportional to 1 ÷ √(time remaining). Half the time left means about 1.4× the daily bleed.

Theta is the direct trade-off for gamma. Long options own gamma and pay theta; short options collect theta and are short gamma. There is no position that gets both, and any strategy claiming otherwise is hiding the risk somewhere else.

Vega: exposure to the volatility number itself

Vega of 0.114 means the option gains $11.38 per contract if implied volatility rises one point — from 20% to 21%.

That figure deserves attention next to the others. A one-point IV move is worth more than two and a half days of theta. IV routinely moves five points around an earnings report, which is $57 per contract from volatility alone, before the stock has moved at all.

This is the mechanism behind "IV crush": buy a call into earnings at 60% IV, the stock moves in your favour, and the option still loses money because IV collapsed to 30% afterwards. The direction was right; the vega was wrong.

Vega grows with time to expiry — 0.195 at 90 days versus 0.055 at 7 — because more remaining time means more opportunity for volatility to matter.

Rho, briefly

Rho measures sensitivity to interest rates: 0.042, or $4.23 per contract per percentage point. For short-dated retail positions it is noise. It becomes relevant for LEAPS and in a fast-moving rate environment.

Reading them as one position

Add up the Greeks across every leg and you have the position's complete risk profile. Suppose you hold ten of these calls:

• Delta +5.40 — equivalent to 540 shares
• Theta −$45/day — the daily cost of holding
• Vega +$113.80 — profit per IV point gained
• Gamma +0.69 — delta rises by 69 shares' worth per $1 up

You now know that a flat week costs $315, that a two-point IV drop costs $228, and that a $5 rally leaves you far longer than you started. That is a position you can manage, rather than a bet you can only watch.