Time Decay (Theta)
Time value is like a melting ice cube: it shrinks every day, and melts faster the closer expiration gets.
Risk warning: forex, CFDs, options, futures and crypto assets usually involve leverage or high volatility, and you can lose more than you put in. This lesson only teaches the concepts; all numbers are for illustration and are not investment advice.
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Text version · Options: Next Steps, lesson 2: “Time Decay (Theta)”
Time value is like a melting ice cube: it shrinks every day, and melts faster the closer expiration gets.
Time value is an ice cube that melts
Time value shrinks every day, and the amount lost each day is Theta. It doesn't melt at a steady pace: the closer the expiration date, the faster it melts.
The buyer's loss = the seller's income
The passage of time works against the option buyer; the premium the seller collected becomes theirs bit by bit as time passes.
At-the-money options melt the most
Theta only eats time value. At-the-money options have the most time value and lose the most each day; deep in-the-money and deep out-of-the-money options have little time value and lose little each day. The higher the volatility, the bigger the ice cube, and the more melts each day.
Key takeaways
- Theta: how much an option's value drops each day.
- Decay isn't steady. At-the-money options melt fastest in the last 30 days before expiration.
- The passage of time hurts option buyers and helps sellers.
- At-the-money options carry the most time value, so they also lose the most dollars per day.
Try it yourself
You can do these exercises in this lesson's interactive simulation:
- Pick 90 days and press ▶: of the $6.41 ice cube, only about $2.82 melts in the first 60 days, but the remaining $3.59 melts in the last 30. Check it with “Remaining time value”.
- Watch “Melted today”: how many times day one's melt is each day in the last week?
- Switch to “You're the seller” and play again: what does the same melting mean for you?
- Raise volatility from 30% to 60%: how much bigger is the ice cube (starting value)? Does “Melted today” grow too?
Quiz and explanations
- 1. When does time value drain away fastest?
- Answer: In the last few weeks before expiration.Theta decay is non-linear and speeds up as expiration approaches.
- 2. Who benefits from time passing?
- Answer: Option sellers.The premium a seller collects gets "banked" as time goes by.
- 3. An at-the-money option is worth $4.00 today with Theta = −0.05 (per share per day). If price and volatility stay put, roughly what's it worth in 10 days?
- Answer: About $3.50 (actually a bit lower).10 days × $0.05 ≈ $0.50, so about $3.50. Theta grows as expiration nears, so it'll actually be a little below $3.50.
Terms in this lesson
- at the money (ATM) (ATM): An option whose strike is about equal to the current stock price.
- expiration date (Expiration): The last day an option is valid; after that, the right is gone.
- premium (Premium): The price of an option, paid by the buyer to the seller; it's the most the buyer can lose.
- Theta: How much value an option loses with each passing day; the decay speeds up as expiration nears.
- time value (Time Value): The part of an option's price above its intrinsic value, reflecting the chance it gains value before expiry; it melts away over time.
- volatility (Volatility): How wildly the underlying's price swings; the bigger the swings, the more expensive options get.
- option writer (Writer): The side that sells an option and collects the premium, taking on the obligation if the buyer exercises.