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Viewer Mail: Larger Moves on Different Stock Options

I received a great question today from Jeremy:

Today, September in the money call options in $TZA had a greater positive mark % change than out of the money call options.
Why is that?

My guess: since they are in the money they are worth more today and since its a first day move down, option buyers are reluctant to buy far out and are choosing to buy in the money instead.
If the downside in the market continues, out of the money should outperform in the money?


Jeremy, welcome to the wonderful world of higher-order greeks.

Your guess is close, but needs a little refinement.

To best approach this question, we need to consider what a call option looks like at options expiration:

This is a p/l graph for a bought call option. We know that at expiration it will be at full loss as long as it is out of the money, and if it goes in the money (plus the premium paid) then you can make a profit.

What we want to concern ourselves with here is the "delta." This is the directional exposure per $1 move in the stock. It can also be viewed as the slope of that line above. Here's the delta at expiration:

We know that at expiration no matter what, the OTM option will have no directional exposure because there's no reason for have it at a positive value-- there's no advantage to owning it. We also know that ITM options are all intrinsic value, which means they will behave like stock and have 100 delta.

Now here's where it gets tricky: we know what the delta of call options will behave like at expiration. But this delta will be different with time left. Therefore, the delta of an option will change over time, and either begin to approach 0 or 100. This is known as charm, or delta decay. Here's what it looks like without my awesome MSPaint skills:

Back to the original question: the Sep $TZA call options have about 2 weeks left to options expiration. There will be a higher relative delta decay on those OTM options, and coupled with the time decay on the value of the option, they have just begun to lose their sparkle.

So when the market moves higher, the OTM options will continue to lose the potential "kick" that they had, say, 3 days ago.

And to top it all off, implied voatility and skew continued to "normalize" which also made ATM calls in $TZA a "less bad" trade than OTM calls.

So it's not that option buyers are hesitant to buy OTM options, its that the mathematical models are starting to reduce the odds as we get closer to opex and as volatility contracts. That's why it's so important to choose the right strikes when you're hedging, otherwise you'll get burnt on the delta decay.

Now if we do in fact start to run higher in TZA, then your OTM calls will move ITM, which will, on a percentage basis, be better than if you had held the original ATM options. But as time continues to pass, the odds of that will decrease.

If you understand charm, then check out my intro into color.

Did you have an 'a ha' moment when reading this post? Imagine that, except for 19 hours in video. OptionFu will make you a great options trader. And yes, we talk about charm, too.

by Steven Place

Steven Place is the founder and head trader at