Moneyness and the time decay curve

Two questions decide most of what an option will do to you: how far it is from the money, and how much time it has left. This lesson gives you a feel for both before the Greeks put numbers on them.

Moneyness

"Moneyness" is just how far the strike is from the stock price, and in which direction. Traders describe it in three ways:

• By label: ITM, ATM, OTM.
• By distance: "$3 out of the money", "6% out of the money".
• By delta: a "30-delta put" or a "70-delta call". Delta is covered in the next module; for now, know that it runs from 0 (far OTM) to 100 (deep ITM), with 50 roughly at the money, so it doubles as a moneyness scale that already accounts for time and volatility.

Delta is the most useful of the three because a $3 OTM strike means something completely different on a $20 stock with a week to go and a $500 stock with a year to go, while a 30-delta option behaves about the same on both.

How moneyness changes what you own

A deep ITM call is a stock substitute: it goes up and down almost dollar for dollar with the shares, and the extra cost over intrinsic is small. An OTM call is a different animal: it does nothing until the stock gets close to the strike, and if the stock does not get there it goes to zero.

The time decay curve

Extrinsic value does not decay in a straight line. For an at-the-money option it follows roughly a square-root-of-time shape: slow at first, faster as expiration approaches, fastest in the last two weeks.

Here is a 90-day ATM option worth $4.00, with XYZ pinned at the strike and volatility held constant. The value at each point is approximately $4.00 × √(days remaining / 90).

 value
 4.00 |*
      |   *  *
 3.00 |         *  *
      |               *  *
 2.00 |                     *  *
      |                          *  *
 1.00 |                               *
      |                                 *
 0.00 +-----------------------------------*---
      90     75     60     45     30     15   0   days left

The first 30 days cost $0.73. The last 30 days cost $2.31, more than three times as much. Holding a long ATM option into the final two weeks is where most of the premium is lost; selling one in that window is where most of the premium is collected. Neither is automatically right, but you should know which part of the curve you are on.

OTM options decay differently

The square-root shape describes at-the-money options. Out-of-the-money options decay in a different pattern: because they need a move just to have any value at expiration, they lose most of their value earlier, as time runs out for the move to happen, and by the last week they are often already close to zero. Deep ITM options have so little extrinsic value that decay barely registers.

A rough picture with 30 days to go, XYZ at $50, volatility unchanged:

The $56 call has lost two-thirds of its value in the first fifteen days and is almost worthless with five days left, while the $50 call has kept 70% of its value at the halfway point. If you buy OTM options, time is against you from day one, not just at the end.

Key idea: At-the-money extrinsic value decays on a curve that accelerates into expiration; the last two weeks cost more than the first two months. Out-of-the-money options lose most of their value earlier, because the move they need is running out of time to happen.

What this means for a trade plan

If you are buying an option because you expect a move, you are paying for time, so buy enough of it that the move has room to happen before the steep part of the curve, and plan to exit before that part. If you are selling an option, the steep part of the curve is where you earn, and it is also where a sudden move hurts most, because there is little premium left to cushion it. Module 5 and Module 7 turn these into rules.

Try it: Take any ATM option with 60 or more days to expiration and note its price. Using the square-root approximation, estimate what it would be worth with 30, 14 and 7 days left if the stock did not move. Then check the actual prices of the same strike at those expirations on the chain. They will not match exactly (volatility differs by expiry), but the shape will be there.

Recap

• Moneyness is the strike's distance from the stock; delta is the most useful way to express it.
• Deep ITM options act like stock, ATM options are all leverage, OTM options are bets that do nothing until the stock arrives.
• ATM extrinsic value decays roughly with the square root of time remaining, so it accelerates into expiration.
• OTM options lose most of their value early because the required move runs out of time.
• Buyers should plan around the steep part of the curve; sellers earn there but have the least cushion.