Every option quote carries a price for the move that has not happened yet and a rate for keeping that bet open. The rate is theta, quoted in dollars per contract per day, so a long option is a position that pays rent whether or not the market cooperates.
Theta is the easiest Greek to read and the easiest to dismiss, because it is usually the smallest number in the row. It also changes shape as expiry approaches, which is why two options with the same delta can be entirely different holds. For a trader who plans to be in the position for a week, the theta column decides more than the entry price does.
Theta as a daily rent
Theta is the change in an option’s price for one day of elapsed time, with the underlying, volatility and rates held still. It is quoted in dollars per share, so a theta of 0.35 means 35 cents a share and 35 dollars per contract per day. Ten contracts at that rate give up 350 dollars a session.
On an option trading at 4.20, 0.35 is 8.3% of the premium per day. Five sessions at that rate removes 1.75, or 42% of what you paid, before the rate itself rises with each passing day. The position has to earn that back through movement: at a delta of 0.45, 0.35 of premium is 0.78 points of favorable move on the underlying, per day, simply to stand still.
The calendar is charged, including weekends. Saturday and Sunday are priced into Monday’s mark, which is why a Friday-to-Monday hold often shows more decay than two weekdays did.
The curve is not a line
Time value falls on a square-root curve. An option’s price scales with the square root of the time remaining, so an option with seven days left carries about 39% of the time value of the same strike with 45 days left, since the square root of 7/45 is 0.39. The same strike at two days carries 21% of the 45-day value.
Daily theta tracks the same shape. On the 45-day call it is 0.031 a day, on the seven-day it is 0.079, and on the two-day it is 0.148. Across the last week the daily rate nearly doubles while the premium it is charged against halves. Against the 45-day option the two-day rate is almost five times larger.
That shape is what a multi-day holder buys. Five sessions taken at 45 days cost about a twentieth of the premium; at seven days they cost nearly half.
What theta costs a multi-day hold
Two calls on the same 100 strike, both at the money with a delta of 0.50, priced off a 100 stock at 20% implied volatility. The figures are illustrative and the stock is held at the strike so only time moves.
| Measure | 45 days to expiry | 7 days to expiry |
|---|---|---|
| Premium | 2.81 | 1.11 |
| Delta | 0.50 | 0.50 |
| Theta per day | 0.031 | 0.079 |
| Five sessions of decay | 0.16 | 0.52 |
| Share of premium lost | 5.7% | 47% |
| Premium left after five sessions | 2.65 | 0.59 |
| Cost per contract | 16 dollars | 52 dollars |
The five-session cost is the change in premium with the stock pinned to the strike, so it is the pure time component: the 45-day option falls from 2.81 to 2.65 across the move from 45 to 40 days, and the weekly falls from 1.11 to 0.59 across the move from 7 to 2 days.
In points of the underlying, the 45-day position needs 0.32 of favorable movement at delta 0.50 to cover its decay. The weekly needs 1.04. One standard deviation over five sessions on a 100 stock at 20% volatility is about 2.8 points, so the weekly’s threshold is not extreme. The timing is the problem: the move has to arrive inside those five sessions, and if it arrives on the fifth the position sits two days from expiry with the steepest decay still ahead of it.
The 45-day option can absorb a late move. It gives up 16 dollars a contract over the week, then still has 40 days of life if the thesis needs another week. On the same dollar risk, the weekly needs a move three times as large in points to cover its decay.
Theta and implied volatility move together
Vega and theta read the same uncertainty from opposite ends. Implied volatility sets both the premium and the daily charge, so an option bid up by a volatility spike arrives with a higher rent attached. The mechanics of that input are in implied volatility; what matters here is that the two costs arrive together.
Take a 30-day, 100-strike call on a 100 stock. At 20% implied volatility it prices near 2.29, with vega around 0.11 per volatility point and theta of 0.038 a day. At 30%, the same strike prices near 3.44 and theta rises to 0.057. The daily cost is half again as large, at the same strike and the same expiry.
If volatility falls back to 20 before expiry, vega takes roughly 1.14 of premium out of the position, 114 dollars a contract, and every day in between was charged at the higher rate. The move has to arrive early enough to cover both.
That pairing is why buying premium after a spike so often disappoints. The size of the premium is explained by the size of the recent range, and the theta it carries makes the trade a bet that the range repeats within days rather than weeks.
Selling theta instead of paying it
Sell the same option and the sign flips. A credit spread, an iron condor, a covered call or a cash-secured put all print positive theta, because the seller collects the rent the buyer pays. The daily figure on the ticket then works for the position instead of against it.
The cost is negative gamma. A short call spread gets shorter as the market rallies, so each point above the short strike costs more than the point before it; a short put does the same on the way down. The position’s delta moves against it precisely when the trade is wrong, and it flattens out when the trade is right, which is the opposite of what a directional trader wants from a winner.
The arithmetic of a five-point-wide spread sold for 1.20 at 40 days: about 0.03 a day of theta, 1.20 kept if it expires worthless, 3.80 of loss at the far strike. Forty sessions of calm earn what one bad session can return three times over.
That asymmetry is the trade. Short theta is paid for quiet and charged for movement, and the charge arrives without an appointment. Anyone selling premium needs a hard exit level on the underlying and a size that survives the maximum loss, because the maximum loss is the number that gets paid when the plan fails.
Spreads cap the loss in exchange for capping the credit, and the choice of width is what sets both. The mechanics are in options spreads.
Choosing expiry from theta
Theta on its own does not rank expiries, because a cheaper option always shows a smaller dollar figure. Divide theta by delta to compare the cost of directional exposure. On those two calls, the 45-day costs 0.062 of theta per delta unit and the weekly 0.158, two and a half times more for the same delta.
For a hold of five to fifteen sessions, the useful part of the curve runs from about 30 to 60 days out. There the daily charge sits near 1% to 2% of premium, the delta stays stable session to session, and a late entry costs less than it would in a weekly.
Inside 21 days the curve steepens. Inside 10 days it dominates the trade. Opening a position in expiration week buys the steepest part of the curve with no time left to be right, and the same five-session hold costs 47% of the premium instead of 6%.
Strike compounds it. A far out-of-the-money option shows small dollar theta and large percentage theta, so the cheap-looking wing of the chain is usually the most expensive per day of remaining life.
Expiry is chosen alongside the strike and the width, and the wider treatment of that structure sits in the swing trading options guide.
The number that matters on your screen
The dollar figure in the theta column means little until it is divided by the premium. A 12-dollar theta on a 900-dollar option is 1.3% a day. A 0.40 theta on an 8-dollar option is 5% a day. The second position has to be right roughly four times sooner, and it is the one that looks cheap at the ticket.
Do that division before the order goes in. For a hold of a week or more, a daily charge near 1% of premium is a position you can sit in. At 5%, the clock decides the exit, and every day that passes without the move turns a small loss into a large one.
The second division is theta by delta, which gives the points of underlying movement needed per day to pay the rent: 0.06 points on the 45-day call, 0.16 on the weekly, and about 1.3 points on the 8-dollar option with a 0.30 delta. That last trade needs a 1.3-point day to break even on time alone.
Both numbers are on the broker’s screen before the fill. The definitions for theta, vega and gamma sit in the glossary when a platform labels them differently. Run both divisions on the two or three expiries you are considering, take the one whose percentage cost you can hold through a quiet week, and let delta and the stop set the size.
