Theta and Time Decay: Why Options Lose Value as Expiry Approaches

Theta is the amount an option’s price is expected to fall over one day if the stock price and implied volatility stay the same. Time decay is not steady: for an at-the-money option it starts slowly and speeds up sharply in the final weeks, so the last month of an option’s life usually costs far more than the first.

In short: an option’s premium is intrinsic value plus time value. Time value is what you pay for the chance that the stock moves in your favour before expiry, and it shrinks to zero by expiration day. Theta measures the daily rate of that shrinkage. Owners of options pay theta; sellers collect it. For an at-the-money option, decay grows roughly with the inverse square root of the time left, which is why a three-month option might lose under 2 cents a day early on and more than 6 cents a day in its final week.

Where time decay comes from

An option’s price, its premium, has two parts (explained in how option premiums work):

Intrinsic value: what the option would be worth if exercised now. A $50 call on a $53 stock has $3 of intrinsic value.
Time value (also called extrinsic value, see time value): everything above intrinsic value.

Time value exists because the stock might move before expiry. A call buyer has unlimited upside and a loss capped at the premium, so more time means more chances for a big favourable move. On expiration day there is no time left, and the option is worth exactly its intrinsic value, or zero. Theta is the daily pace at which time value drains away. It is one of the five Greeks covered in option Greeks explained.

Theta is usually quoted per share per calendar day, as a negative number for an option you own. Multiply by 100 for a standard contract.

A worked example: decay of an at-the-money call

Hypothetical Maple Widgets Inc. trades at $50, and the stock price does not move. We price a $50 call with the Black-Scholes model, using 30% implied volatility, a 4% interest rate, no dividends, and exact calendar-day counts.

Days to expiry	Call price	Theta (per share per day)	Theta per contract
90	$3.21	minus $0.019	minus $1.90
60	$2.58	minus $0.023	minus $2.28
45	$2.22	minus $0.026	minus $2.59
30	$1.80	minus $0.031	minus $3.12
21	$1.49	minus $0.037	minus $3.68
14	$1.21	minus $0.045	minus $4.45
7	$0.85	minus $0.062	minus $6.19
3	$0.55	minus $0.093	minus $9.31
1	$0.32	loses all $0.32 by expiry	loses all $32

What the table shows:

From 90 to 60 days, the call loses $3.21 minus $2.58 = $0.63, about 19% of its starting value.
From 30 days to expiry, it loses the remaining $1.80, about 56% of its starting value.
Theta per day more than triples between 90 days and 7 days (from 1.9 cents to 6.2 cents).

The square-root rule of thumb

For an at-the-money option, time value is roughly proportional to the square root of the time left. One third of the time left should leave about the square root of one third, or 58%, of the value: $3.21 x 0.58 is about $1.85, close to the model’s $1.80 at 30 days. Because the square root curve is steepest near zero, decay accelerates as expiry nears.

Moneyness changes the shape of decay

Out-of-the-money and in-the-money options decay differently, because they have less time value to begin with.

Out of the money: a $55 call

Days to expiry	Call price	Theta per share per day	Daily decay as % of price
90	$1.37	minus $0.016	1.2%
60	$0.86	minus $0.018	2.0%
30	$0.33	minus $0.018	5.4%
14	$0.07	minus $0.013	17.5%
7	$0.01	minus $0.005	about 50%

In dollars, the out-of-the-money call’s theta peaks earlier and then fades, because there is less and less left to lose. In percentage terms the decay is brutal: with two weeks left, a stock still sitting at $50 erases a sixth of the option’s value each day. Cheap, short-dated, out-of-the-money options look inexpensive per contract, but they lose value the fastest in relative terms.

In the money: a $45 call

Days to expiry	Call price	Intrinsic value	Time value
90	$6.33	$5.00	$1.33
30	$5.35	$5.00	$0.35
7	$5.04	$5.00	$0.04

Most of this option’s price is intrinsic value, which does not decay. Only the $1.33 of time value erodes. Deep in-the-money options behave more like the stock and less like a bet on time.

Theta from the seller’s side

Every dollar of theta an option owner pays is, before costs, a dollar the seller collects. A seller of the 30-day at-the-money call above has positive theta of about $3.12 per contract per day. That is why time decay is often described as working “for” sellers.

The catch is that theta is not free. It is the market’s price for bearing gamma risk: the risk that the stock moves sharply and the short option’s losses grow faster than linearly. Gamma rises in the same final weeks that theta does, as covered in gamma explained. The seller of a 7-day at-the-money call collects about 6 cents a day, but an immediate $3 jump in the stock would raise the call’s price from $0.85 to above $3, a loss of more than $2.20 per share, which is more than a month’s worth of that decay. Selling options is not a reliable source of income; it is a trade of steady small gains against the possibility of large losses.

Theta rises with implied volatility

Theta is larger when implied volatility is higher, because there is more time value to lose. Holding everything else fixed, here is the 30-day at-the-money $50 Maple Widgets call at three volatility levels:

Implied volatility	Call price	Theta per share per day	Theta per contract
20%	$1.23	minus $0.022	minus $2.18
30%	$1.80	minus $0.031	minus $3.12
45%	$2.65	minus $0.045	minus $4.54

That is why options on volatile stocks, or on any stock just before earnings, bleed faster if nothing happens. It also connects theta to vega: when implied volatility falls, the option loses value immediately (vega) and then decays more slowly afterwards (lower theta), as described in implied volatility explained.

Puts, and the odd case of positive theta

Puts decay the same way as calls in most cases. One exception: a very deep in-the-money European-style put can have slightly positive theta, because its value is mostly the discounted strike, and that discount shrinks as expiry approaches. A three-month $70 put on a $50 stock has a theta of about plus $0.006 per day in the model. For American-style puts, which can be exercised early, the holder would usually exercise instead.

Weekends, holidays, and how theta is quoted

The model above counts calendar days. Some platforms quote theta in trading days instead, which makes each day’s number larger. Either way, markets generally price in a known weekend ahead of time, so an option does not usually drop by three days of theta at Monday’s open just because the weekend passed. If you see a different theta on two platforms, the day-count convention and the implied volatility input are the usual reasons.

What can go wrong

Being right too slowly. A call buyer can correctly predict a stock will rise and still lose money if the move comes after most of the time value has decayed.
Confusing cheap with good value. The table shows short-dated out-of-the-money options losing a large share of their value daily. A low price per contract is not a margin of safety.
Theta is not the whole story. A change in implied volatility can wipe out or exceed weeks of theta in a single day, for example after an earnings announcement.
Sellers face gaps. Collecting theta every day does not protect against an overnight move that produces a loss many times the premium collected.

Time decay is one of the main reasons the academic evidence shows retail options buyers losing money on average, discussed in why most options buyers lose.

Takeaway

Theta is the daily cost of holding an option’s time value. It is small and steady for long-dated options and grows rapidly in the final weeks, especially for at-the-money contracts. Out-of-the-money options lose the largest share of their value per day near expiry, and in-the-money options decay least because most of their price is intrinsic value. Sellers collect theta, but only by taking on the gamma risk that comes with it.