Delta: A Primer

Weeks ago, I wrote a thread talking about gamma.

Let’s talk about its parent greek, delta, and why it matters to you.

What is delta?By definition, delta is the rate of change of an option’s price relative to a $1 move in the underlying stock.Delta for OTM options is lower than the delta for ITM options, and ranges between 0.00 and 1 (-0.0 -> -1.0 for puts), with the ATM delta being .50 on either side. Some brokers will display this delta as whole numbers, others a decimal, but it’s the same delta. (IE: 50 delta = .5)This roughly represents how much the price of your option will change with that $1 move. If you have a .4 delta option, and the underlying share price moves up $1, your contract will gain ~$40 in value. If it moves down $1, your contract will lose ~$40 in value. How much this delta changes is due to gamma, which I’ve written several short posts upon.

Back to delta. If you buy a $50 call on XYZ while it’s trading at $50, you will have .5 delta. If XYZ moves upward 10% to $55, your theoretical delta value will be .85. If the underlying moves from $55 to $56, your contract will gain ~$85.As contract expiration approaches, it becomes much easier to hit 1 delta of movement (gamma is also highest at expiration). This is another reason why weeklies and 0dte’s return so well, and another reason why, if playing earnings, you should buy 30+ days out if you can afford toThis is the delta for the March 14th expiration on SPY. $5 ITM at $412 (SPY $417), delta is near 1.
For an expiration in two weeks, that much delta is way further ITM, at the $370 strike.

This “decay” is known as charm. Charm is the sensitivity of an options price to small changes in underlying price, and passage of time. It’s the differentiation of delta and theta, or DdeltaDtime. I’ll talk about charm in another thread.The acceleration of delta into expiration is also reflected by gamma, which increases into expiration (I talked about it in the linked thread above)

Why does delta matter, though? Isn’t it just telling us how much our contract is increasing/decreasing when the underlying moves? Yep, in short, you’ve got it. But what else is there?

Delta can be used as a pseudo-estimator of the probability a contract will be in the money at expiration. Naturally, an ATM call option will have .5 delta, which gives the option a 50% chance of being ITM at expiration. This isn’t a perfect probability, and works better in specific situations, but is a good approximation, nonetheless. Now, what does delta tell me?

Well, intraday Delta can tell you direction, specifically with direction of indexes and other liquid tickers, as written about in the NOPE thread here.

But what does long term delta tell me?

Delta tells you how exposed you are to movements in the price of the underlying.

If you long a $50 call on XYZ trading at $50, you have .5 delta, to hedge that positive delta, you would, theoretically, short 50 shares of the underlying.This allows thetagang and volgang to prosper.

However, if you're a directional trader, delta neutrality is not your best friend, since it takes directional movement completely out of the equation.Long puts and short calls will have negative delta, and long calls and short puts will have positive delta. You can build complex strategies that achieve high delta no matter where the underlying is, so those quick moves can make you some $.You also can use these to your advantage to create option strategies that mimic movement of 100 shares of stock, at a fraction of the price (see: synthetic longs/shorts)

That's about all that I have for delta, in a nutshell.

If you have any questions or comments, or want to tussle, please PM me on twitter @falcon_fintwit

Hope you learned something today :)