Special Edition: Down Under the Delta Neutral
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| Author       | Source       | 
| :-------------: |:-------------:|
|  [u/yelyah2](https://www.reddit.com/user/yelyah2/) | [Reddit](https://www.reddit.com/r/Superstonk/comments/ok4chd/special_edition_down_under_the_delta_neutral/) | 

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[Possible DD 👨‍🔬](https://www.reddit.com/r/Superstonk/search?q=flair_name%3A%22Possible%20DD%20%F0%9F%91%A8%E2%80%8D%F0%9F%94%AC%22&restrict_sr=1)

Here we go, here we go! We are under the Delta Neutral (DN).... I repeat... we are under the Delta Neutral...

This is where I trade this indicator, and we are in my world now.... the Upside Down DN World....

[![r/Superstonk - Special Edition: Down Under the Delta Neutral](https://preview.redd.it/7cylj5x1k6b71.png?width=1195&format=png&auto=webp&s=ff5babd2fac7b7b66abf0a416ca2e2484c10f7f4)](https://preview.redd.it/7cylj5x1k6b71.png?width=1195&format=png&auto=webp&s=ff5babd2fac7b7b66abf0a416ca2e2484c10f7f4)

do do doooo.....

I've been showing you the log-based 10 graphs lately, because nothing super exciting has been happening, but here's a graph showing the DN up close and personal, showing we closed under the DN yesterday!

[![r/Superstonk - Special Edition: Down Under the Delta Neutral](https://preview.redd.it/9ftbjem0k6b71.png?width=910&format=png&auto=webp&s=0916d523cf593eaf2737a62a5f8e8155e0ec4270)](https://preview.redd.it/9ftbjem0k6b71.png?width=910&format=png&auto=webp&s=0916d523cf593eaf2737a62a5f8e8155e0ec4270)

GME 1/6/2021 - 7/13/2021

For Part I of this post, let me take you all the way back to FEBRUARY 2021.... the last time it happened...

PART 1 - THE FEBRUARY TRIP BELOW

It was a dark time... money lost... sanity drained... FUD everywhere... We all clung onto our hopes, DD, and each other. We all have our memories of that time long ago, and mine are held through the lens of the DN World.

Let's see what happened:

-   First, the price tanks. Pick your reason why. We aren't covering that now.

-   As the price tanks, hedgies are selling off loads of shares based on their OI, and helping the price continue to drop hard.

-   As the price drops below the delta neutral, the IV is suppressed very quickly, as shown in the graph below. It also tanks from ~10.0 to bouncing around 1.0-3.0 within a WEEK

    -   Check what happens when the price tanks in March. The IV has an initial spike, the settled into a 2.0-4.0 range for FIVE weeks before settling down further.

[![r/Superstonk - Special Edition: Down Under the Delta Neutral](https://preview.redd.it/vonx8y6zj6b71.png?width=910&format=png&auto=webp&s=278e95650859b24575f3a813ca324a89b8852849)](https://preview.redd.it/vonx8y6zj6b71.png?width=910&format=png&auto=webp&s=278e95650859b24575f3a813ca324a89b8852849)

GME 1/4/2021 - 7/13/2021

-   The IV also tanks under the DN, and ATM prices suddenly go on discount. The 30-day ATM prices go from $130-$155 at the peak (~40% of Underlying Price), to $6-$11 by 2/5 (~10% of Underlying Price).

-   Call Prices are often lower than Put Prices at this time. Call prices look tasty to investors, because... STONKS GO UP! This is why stocks generally sit on top of the delta neutral. There are generally more call buyers than put buyers.

Quick palette cleanser before we move on?

[![r/Superstonk - Special Edition: Down Under the Delta Neutral](https://preview.redd.it/qvbe41sxj6b71.png?width=656&format=png&auto=webp&s=8a659858dc3d25f1eb699a17dd7bedf8399b22fc)](https://preview.redd.it/qvbe41sxj6b71.png?width=656&format=png&auto=webp&s=8a659858dc3d25f1eb699a17dd7bedf8399b22fc)

yummmm

Ok, let's continue....

-   By the crash, the put OI is monstrously huge. I know there's a lot of debate around this right now. My personal opinion is it's a mix of the following:

    -   Come on.... the price went from ~$10 to almost $500 in a couple of months. People thought this thing was going to crash back down after it squeezed. It was a safe bet to buy puts on it. Not everything against GME is nefarious...

    -   I said not EVERYTHING.... There is some craaazy OTM put volume/OI during the January squeeze, that correspond to increase in those put prices, and the volume / OI ratio is waaaayy high. Again... personal conjecture here... but what if Citadel HF was selling those puts to Citadel MM, and Citadel MM executed their OTM positions, effectively forfeiting their premium. What does this do? It allows Citadel MM to give a cash injection to Citadel HF on the open market, gets around their firewall separating the two entities, and can take advantage of Citadel MM special privileges.

    -   I've heard all kinds of theories on other strategies for those OTM put OI's, and for me, it always comes back to: * No, they're not going to do any strategy that involves buying a ton of stocks (*cough* married puts *cough*), because the point is they shorted it a ton, the stocks are hard to come by, and it's really expensive to do. * Who's buying those teeny Puts? There are a lot of reasons someone would want to sell those puts, which is what most explanation boils down to. Hell.... I'd love for someone to buy a load of $0.50 puts from me, but seriously... who's buying them? That's how I came to the theory above. * Feel like there's going to be some fights over this, but let's be honest... no one actually knows the answer to this question, it's all theories at this point.

-   The Call OI has now dropped from 47% on 1/22 to 14% by 2/1. However, once the price drops under the DN, the Call OI starts building up fast, as in 35% - 66% increases within each week, while the put OI only increases around 0% - 2% each week, which makes the Call OI bangs up to 25% by the February bounce.

Ready to find out what that fast build-up of Call OI did?

or do you want another palette cleanser?

[![r/Superstonk - Special Edition: Down Under the Delta Neutral](https://preview.redd.it/wbzkwf9wj6b71.png?width=760&format=png&auto=webp&s=e0f5ac2937910087161c4c02f84440736752e0bd)](https://preview.redd.it/wbzkwf9wj6b71.png?width=760&format=png&auto=webp&s=e0f5ac2937910087161c4c02f84440736752e0bd)

raaaawwwrrr

Sorry... those come with the territory....

-   Ok, so as all those people are buying up calls, the total market delta is going up, and hedgies are buying up more and more stocks because of it.

    -   If you recall a few posts ago, I talked to you about the build-up of the total market delta. If you don't remember, [here's my post](https://www.reddit.com/r/Superstonk/comments/o9qb4n/delta_neutral_update_any_meaningful_underlying/), or check the bottom for the details.

The graph below summaries the total market delta share equivalents (dark blue) versus the underlying close price (green).

[![r/Superstonk - Special Edition: Down Under the Delta Neutral](https://preview.redd.it/vqfw7iuuj6b71.png?width=909&format=png&auto=webp&s=d81c3c58fe8eb0b3681407952987199d6bc330f3)](https://preview.redd.it/vqfw7iuuj6b71.png?width=909&format=png&auto=webp&s=d81c3c58fe8eb0b3681407952987199d6bc330f3)

GME Total Market Delta Share Equivalent versus Underlying Close

You'll notice that total market delta increased significantly BEFORE the January and February/March squeezes. This helped to contribute to the buying pressure to push GME upwards.

Ohhh and who do we have here? It's our good friend, GAMMA!!

High ATM Gamma Factors makes everything nice and squeezy. Those factors increase right before significant increases, as shown in the table below.

[![r/Superstonk - Special Edition: Down Under the Delta Neutral](https://preview.redd.it/hwhh2hbtj6b71.png?width=910&format=png&auto=webp&s=86f8529521c1bf8ed2ce170fd349bf62618af04a)](https://preview.redd.it/hwhh2hbtj6b71.png?width=910&format=png&auto=webp&s=86f8529521c1bf8ed2ce170fd349bf62618af04a)

GME Close/DN/ATM Gamma Factors

Then once the Underlying Close Price hits the Gamma Maximum point and...

[![r/Superstonk - Special Edition: Down Under the Delta Neutral](https://preview.redd.it/c8nc9y4pj6b71.png?width=2598&format=png&auto=webp&s=3f2a8b7c1074a129bc4c912dbe0bcec665471779)](https://preview.redd.it/c8nc9y4pj6b71.png?width=2598&format=png&auto=webp&s=3f2a8b7c1074a129bc4c912dbe0bcec665471779)

BOOOOMMM!!!

Ok, so all kinds of things happened in February, but I wanted to walk you through the general Life Cycle of stocks under the DN, using GME as an example.

TLDR - Part 1:

The life cycle of a stock under the DN generally consists of the following parts:

-   Underlying price drops below the DN

-   IV decreases

-   Call/Put prices decrease

-   Stock price just dropped + stonks go up + calls look tasty = higher call buying

-   Options sellers buy up stocks to hedge

-   If you're lucky, your good friend Gamma shows up

-   Bing, bang, boom, you're back over the DN.

PART 2 - STARTING THE JOURNEY BELOW

As we start on this adventure below the DN together, just remember that we are in this together and to always pay the ferryman.

Let's quickly remind ourselves what's happening now:

[![r/Superstonk - Special Edition: Down Under the Delta Neutral](https://preview.redd.it/yttusvynj6b71.png?width=910&format=png&auto=webp&s=dbd870b866a4c302612bd3bce967c6c9f1a7e9fe)](https://preview.redd.it/yttusvynj6b71.png?width=910&format=png&auto=webp&s=dbd870b866a4c302612bd3bce967c6c9f1a7e9fe)

-   The price closed at $180.06 yesterday, compared to the DN of $188.

-   The ATM put volatility dropped from 1.2 to 1.09 (lowest since 5/11), and I suspect the ATM call volatility will follow soon.

-   The ATM option prices dropped around 5% today

-   The total market delta equivalent shares is dropping with the price, and accelerating the drop as option sellers and selling off more and more shares

-   The ATM gamma factor is low right now, and nothing particularly interesting is going on with the other gamma indicators

How long will this take?

-   Retail could storm in at pre-market and buy the dip to bring it out straight away, and it would have nothing to do with these indicators.

-   If hedging controls the volume, then it usually reverses in 1-3 days. When I trade this indicator, I plan for returns to be worth holding for 2 weeks.

-   It is not common for stocks to sit under the DN for as long as GME did back in February, but we all know GME is a special one!

Watch the following to signal a reversal:

-   A drop in IV/option premiums

-   High call % volume/OI

-   I'll be watching the other indicators, and will report anything interesting

[![r/Superstonk - Special Edition: Down Under the Delta Neutral](https://preview.redd.it/2telmucmj6b71.png?width=533&format=png&auto=webp&s=d8566faa09d186ce9b64db87c8a9f021a2a575eb)](https://preview.redd.it/2telmucmj6b71.png?width=533&format=png&auto=webp&s=d8566faa09d186ce9b64db87c8a9f021a2a575eb)

To the moon for us all!

TLDR - Part 2:

-   Hold tight

-   This part is fun

-   Watch options if you want

*Now it's time to tell you all the boring stuff....*

[![r/Superstonk - Special Edition: Down Under the Delta Neutral](https://preview.redd.it/bm1l5jikj6b71.png?width=1200&format=png&auto=webp&s=9a704e70bacf00d1f0fafeb6f144a1faf56b47fd)](https://preview.redd.it/bm1l5jikj6b71.png?width=1200&format=png&auto=webp&s=9a704e70bacf00d1f0fafeb6f144a1faf56b47fd)

wah waahhhh

Overview

In general, all stock indicators boil down to two things - reversion to the mean and momentum. Every trader wants to accurately predict these two forces better than other guy, and if you use different indicators than the other guy, that an give you an 'alpha' in trading if it's a better predictor.

I make a lot of different indicators, but the two primary ones are the Delta Neutral and Gamma Neutral:

-   Delta Neutral (DN) - This helps identify reversion to the mean, and represents the underlying price that would create a total market delta of 0 across all GME options (all expiration dates) for a given date. In general, it acts like a floor to the underlying price, but if the price drops below the delta neutral, then it tends to shoot back up above that line.

    -   This is generally how I trade my model. I watch for stocks that drop below the DN, and buy them, expecting for traders to identify that the stock is underpriced and will revert back to a higher level.

-   Gamma Neutral (GN) and Gamma Maximum (GM) - This helps identify momentum. The GN represents the underlying price that would create a total market gamma of 0 across all GME options (all expiration dates) for a given date, whereas the GM represents the underlying price that would create the maximum gamma across the market.

    -   In general, a sudden increase in gamma indicates a sharp upward in momentum that continues until that gamma drops.

    -   The GM seems to act like a ceiling, but fun things happen when the underlying crossing that threshold!

This is my own personal 'alpha' that I developed for my own trading purposes, and am sharing with this community because it's given me back so much. This is not financial advice. I'm just a mathematician that likes to play with options data, and I am not a professional trader.

*Methodology and Assumptions*

Delta

The Delta of an option represents the expected change to an option's price based on a $1 change in the security's underlying price. For example, if the GME underlying price is at $100,000,000 and a GME $102,000,000 strike call has a delta of 0.2, then that call option price will increase by $0.2 if the GME underlying price moves up to $100,000,001. Note that the price is also affected by gamma so will actually be higher than the $0.2 price increase estimated by delta, which will be covered later.

Delta hedging is a trading strategy employed by market makers (MM's) to minimalize the directional risk associated with price movements in the underlying security. Traditionally, you can think of a MM buying 20 (0.2 x 100) stocks of the underlying security if the price increases by $1 (using the example above). However, it's important to note that hedge funds often use other derivatives to hedge, not just buying/selling stocks because it requires less capital to do so. However, these indicators can be used as a directional proxy for some of the MM behavior as the underlying price increases/decreases.

The total market delta share equivalent represents the sum of delta x OI across all strikes/expiration prices in a given trading day. I will say it one more time, hedge funds are not actually holding this number of shares on a given day to hedge. They often hedge with other market derivatives. However, it can give us an indicator for hedge funds buying/selling underlying equity relativities.

Delta Neutral

The Delta Neutral price that creates a total market delta of 0 across all GME options (all expiration dates) for a given date. It can also be though of as the intersection of a supply/demand curve for hedged stocks. See the "Methodology and Assumptions" section for full detail on how I develop this indicator.

Notes below for general options on how the delta neutral interacts with the underlying price:

-   There is a large influx of call option purchases, because:

    -   The call prices get less expensive as the underlying price approaches the delta neutral

    -   Stock prices usually rebound/revert back to the mean after large crashes, so the price often rebounds anyways.

-   With the large influx of call volume, market makers have to start buying stocks to delta hedge, which turns the price back around and creates an upward trajectory.

    -   Important note that hedgies often hedge with derivatives instead of buying stocks, so there isn't a 1-to-1 relationship between the delta and shares bought/sold by hedge funds.

-   Historically, you can see that GME often bounces off the delta neutral prices during drops. The exception is the February drop. When the underlying goes below the delta neutral price, a lot of pressure builds up that results in a significant increase when that pressure is released.

    -   Note this is the primary way that I trade my model. I made a scanner that looks for equities that fall below the delta neutral.

Gamma

The Gamma of an option represents the rate of change of the Delta of an option with respect to a $1 underlying price movement. From our example above, if the GME underlying price is at $100,000,000 and a GME $102,000,000 strike call has a delta of 0.2 and a gamma of 0.05, then that call option price would actually increase by $0.25 (0.2 + 0.05) if the GME underlying price moves up to $100,000,001.

MM also hedge against gamma risk, but the impact of buying/selling securities to hedge is often much lower than the impact of delta hedging (also remember that they use derivatives to hedge too). However, you are probably familiar with gamma because of the "gamma squeeze" that happened back in January. A gamma squeeze happens when the underlying stock price begins to go up very quickly in a short period of time. This forces more buying activity from rapidly increasing deltas/hedging, which continues to inflate the price.

Gamma Neutral/Maximum

The Gamma Neutral price that creates a total market gamma of 0 across all GME options (all expiration dates) for a given date. The Gamma Maximum price creates the maximum total market gamma across all GME options.

General notes below for observations on how the Gamma Neutral indicator behaves:

-   It acts like support/resistance between the delta neutral and the underlying, and typically bounces around between the two prices for most symbols (like we have seen with GME since April).

-   It also goes crazy in periods of high volatility, as you can see by the very higher spikes.

-   A gamma spike indicates the presence of POTENTAILLY slippery option market conditions, which COULD lead to a gamma squeeze. There were certainly spikes present back in January, but we had a few one-day false starts this last month.

-   They are often triggered by high price movement in a day, which can lead to continue high growth if underlying volume supports it.

-   Gamma spikes can also be triggered by unusual options purchases during the day. These are the one ones to find, because you can often catch the high increase waves before they actually start.

-   If I'm trading this indicator, I often either wait for a gamma spike to continue for 2 days in a row and supported by increased volume. Otherwise, I invest straight away if I find a gamma spike just based on options movement (i.e. no significant underlying increase yet).

General notes below for observations on how the Gamma Maximum indicator behaves:

-   It generally acts like a ceiling for the underlying stock value

-   However, when the stock breaks through the gamma maximum, fun things happen!

Methodology

I write my own algorithms to produce the results above. The following lists some key methodology and assumptions I use:

-   I rely on daily options and stock summaries produced by [www.historicaloptionsdata.com](http://www.historicaloptionsdata.com/)

-   For the Implied Volatility (IV), I use the following method:

    -   Calculate the raw IV of the mid-point between bid/ask price at close.

    -   Calculate a "blend" IV, which represents the IV where the call/put parity holds, i.e. where call delta -- put delta = 1, using the same IV.

    -   Smooth the mid-point call/put and blend IV using a gaussian smoothing algorithm with a 20-strike window.

    -   Apply the smoothed call/put relativities to the smoothed blended IV curve

    -   Fill any missing values with a linear interpolation of the neighboring strikes.

-   Using the final call/put IV estimates described above, I calculate my own Greeks. I like this source if you're interested in the formulas: <https://www.macroption.com/option-greeks-excel>

-   For the total market delta and total market gamma, I rely on the OI x delta and OI x gamma for each strike price.

    -   Note that the delta of a call is usually equal to (1 - put delta), so not adjustment is needed to the delta signs when calculating the total market delta.

    -   However, the call/put gammas are both positive based on the B-S calculation. If you're calculating the total gamma for a portfolio, or the total market, you have to add the call gamma and subtract the put gamma.

-   To estimate the delta neutral and the gamma neutral, I have an algorithm that relies on the optimization toolbox in Matlab to identify an underlying price that achieve a total market delta and a total market gamma.

-   Note that the IV would change with higher/lower prices for the delta/gamma neutral and the sensitivity tests, but the impact is not significant enough to make a meaningful difference and takes significant processing time to apply the IV curves. However, it is an important simplifying assumption to be aware of.

-   Open Interest (OI) is always lagged one day for options summaries. The OCC releases final open interest on a given day, and it represents the OI for the close of the prior day. Therefore, the OI I get in my summaries on 6/28 does not represent the OI as of close on 6/28. It represents the OI as of close on 6/25. If you see a source like Yahoo give live OI throughout the day, they are only estimates, and their algorithm methodology for estimating the OI based on various price/volume movement is a closely guarded secret. Using the prior day OI is currently a limitation of the data available to me.

*Disclaimer: With the recent debate on the sub, I've decided to label my posts as "Possible DD" until someone is able to peer review my work, and independently replicate it. So far, my only proof has been how it works in the field, which means it should not be blindly taken as truth. I think every writer should hold themselves to their own standards, and no one else's. Every aspect of my work is peer reviewed in real life, so this is my own standard. It's also the responsibility of every reader to judge the quality of content they read, and don't take anything at face value. To the moon for us all!*
