Let's consider the theta measures the impact of the passage of time on the option premium.

All else being equal both calls and puts lose value as time goes by and expiry gets closer.

That's because the time value of an option decays over time.

From a buyer's perspective, this means a long option.

Position carries negative theater.

Tomorrow your option will generally be worth a little less than today, simply because there's less time left to expiry in mark to market terms.

That's a drag on your profit and loss.

For sellers, it's the opposite.

Theater represents the steady compensation they receive as time passes.

This is why theater is often described as the running yield or carry of an option position.

Here's an analogy. Owning an option is like renting insurance.

Every day you hold it, you pay a little bit of rent in the form of time decay.

The seller on the other side collects that rent as income for providing the protection to you.

Now, if you look at the charts on the screen, you can see how this plays out on the left hand charts.

Theta is most negative for at the money options and the closer we are to expiry the steeper that dip becomes on the right hand surface plots, you can see the same idea in three dimensions.

Theta spikes downwards for at the money options as expiry approaches.

While for deep in the money or deep outta the money options, theta values are close to zero.

Notice how this pattern looks like the mirror image of gamma, and that's no coincidence.

Gamma is what makes options risky and non-linear.

It measures how sensitive delta is, which makes hedging more complex.

Theta, on the other hand, can be seen as the cost of carrying that gamma exposure.

Buyers pay it through time decay while sellers earn it as compensation for taking on gamma risk.

And this connection becomes clearer when you think about trading strategies.

If your long gamma, you benefit from realized volatility, but you are paying for that convexity through negative theater every day.

If you are short gamma, you collect positive theater as income, but you are exposed to losses if the market moves too much.

In other words, gamma and theater are two sides of the same coin For a single vanilla option.

Long gamma always comes with short theater and short gamma always comes with long the, so the trade off is simple but powerful.

Do we want to pay rent every day in the hope that volatility bails you out, or do you want to collect rent every day while taking the risk that the market suddenly breaks out?