Options Time Decay

option decay

This graph depicts the changing gamma for an option over time. We may notice that at the red arrow, we have the most gamma. These are the short-dated ATM options. At the green circles, we have the least gamma for the short-dated far OTM options.

If it sounds familiar, it is because it is the same as our time decay graph. Wherever theta and time decay is the highest, gamma is also the highest. We will use the graph above and a stock trading at 190 as an example. A 205 call option expiring in five days is not going to have much value. Perhaps it worth 5 cents.

Theta has to be low because the option is only worth 5 cents and cannot lose more than that. Gamma is also small because it makes almost no difference if the stock moves from 190-191. The option is still next to worthless. Conversely so for the 205 call expiring in 45 days.

It still has some value and thus will experience theta decay while also having some exposure to gamma. After all, there is still a chance the stock could move from 190-205 in 45 days. It is highly unlikely to do so in just five days.

Over/Under on NFL Sunday 

Imagine it is NFL Sunday and the over/under for the game between the Chiefs and Bucs is set at 50. That means that there are two choices. Bet on the over if we think more than 50 points will be scored (gamma) or bet on the under (theta). Say that we bet the under. The game starts. Immediately as the game gets underway, we start to notice we are collecting money and the live odds are slowly moving in our favor.

The new over-under is 48. Why? Nothing has happened yet, after all. This is our theta collection in action. As time ticks off the clock, we are collecting theta, albeit slowly. The teams punt a few times but all of a sudden, touchdown. The new over-under is 52 and we are losing money. This is our negative gamma working against us.

Now imagine the game progresses and it is an unmemorable performance. We are late in the fourth quarter and the score is 10-3. At this point, it is irrelevant whether a touchdown is scored because there is simply not enough time for the score to reach 50. Our gamma is reduced to almost nothing, along with our theta. We are thus at the green line and circles on the above graphs.

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Disclaimer: The information above is for educational purposes only and should not be treated as investment advice. The strategy presented would not be suitable for investors who are ...

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