Which Greek measures the fear, and which measures the clock?
Delta and gamma handle the stock price. Two more Greeks handle the other two things that move an option: how much movement the market expects, and how much time is left. They are vega and theta, and for an option buyer they pull in opposite directions every single day.
Vega — the price of expected movement
Vega = the change in the option's price per one percentage point of implied volatility.
Take the 30-day at-the-money $100 call from the last lessons: IV 20%, premium $2.30, vega 0.11.
- IV rises from 20% to 30% → +10 points × 0.11 = +$1.10 → premium ≈ $3.40.
Cross-check with the approximation from Unit 2: 0.4 × 100 × 0.30 × 0.287 ≈ $3.44. The Greek and the formula agree, because the Greek is the slope of that formula.
Two properties worth carrying:
- Vega grows with time. It scales with √T. A one-year at-the-money option on the same stock has vega around 0.40 — roughly seven times the vega of a one-week contract (√(365/7) ≈ 7.2). Long-dated options are volatility positions far more than they are direction positions.
- Vega peaks at the money, for the same reason time value does.
Theta — the clock, in dollars
Theta = the change in the option's price per day of time passing, holding everything else constant. It is negative for buyers.
Same contract, 30 days out at $2.30. One day passes with nothing else changing and it is worth about $2.26. Theta ≈ −$0.04 per share = −$4 per contract per day.
Now run the clock down. With 5 days left, that option is worth roughly $0.94, and one more day takes about $0.10 — theta ≈ −$0.10, roughly two and a half times faster than at 30 days. That is the acceleration from the decay lesson, now expressed as the Greek that measures it.
The two of them together
For a buyer, this is the deal: you pay theta every day to hold the vega and gamma you bought. The position only pays if movement arrives before the clock takes the premium. That is the honest description of every long option — a race between movement and time, with the entry price set by someone who priced the race.
And this is why the earnings trap in Unit 2 hurts so specifically. Buying just before a report gets you high vega at a high price. After the report, the volatility crush hits your vega while theta has been running the whole time. Two Greeks against you at once — the arithmetic behind "I was right about the direction and still lost money."
Rho, briefly
Rho measures sensitivity to interest rates. For short-dated equity options it is small enough to ignore in practice. It matters for long-dated contracts and in periods of large rate moves. Know the name; move on.
In the data
Theta is published beside delta and gamma on the chain. Apple's is below, in the Terminal's options view, as the Θ column; the chain's Greek columns stop there, so vega has to be estimated.
Open Apple's chain with IV and the Greeks in the EODHD Terminal
Neither Greek has one universal scale. Theta can be quoted per calendar day, per trading day or per year, and vega per point of volatility or per one per cent change in it. Comparing one contract's theta with another's on the same screen is safe; reading a single number as "dollars per day" is an assumption you supplied. The share price in the table is the spot for the vega estimate in the exercise.
Try it now
In the chain above, take the at-the-money strike at a near expiry and at one six months or more out, and read theta for both. Estimate each contract's vega from the approximation above: 0.4 × spot × √(days to expiry ÷ 365) ÷ 100 per point of IV, with spot the last price in the table. Confirm the long-dated vega is several times larger, the near-dated theta larger in magnitude.
Take the near-dated theta and multiply by 100. Write the sentence: "Holding this contract costs me about $___ per day if nothing else changes." That number is the rent on the position.
Multiply vega by 100 and ask what a 5-point IV move would do in dollars. Compare it with a full day of theta. On a short-dated contract before an event, vega usually dwarfs theta — and after the event, it reverses on you.