Max Pain: A Story of a Dog and his Tail


Howdy Superstonk,

In my previous DD’s I have begun investigating how the options chain for GME has historically correlated with the price of the underlying stock, and what it means for price discovery. You can find these DD’s below.

It Takes Money to Buy Whisky: Distilling GME’s Options

It Takes Money to Buy Options: Distilling GME’s Whisky

Additionally, for those that are interested, I previously wrote about the DTCC Continuous Net Settlement (CNS) system, which has been getting some renewed interest in the sub, so it may be of interest to newer members.

T+69

After exploring the relationship between options chain delta and GME price, I got a lot of great questions about max pain, so I decided to start digging into it. Primarily, I wanted to investigate the long held belief on this sub that options writers are manipulating the price of the stock to inflict maximum pain on retail options buyers. Do market makers simply take the money from options buyers through stock price manipulation, or are the options buyers dictating the price of the stock through market maker hedging? Does the dog chase the tail or the tail chase the dog?

Intro to Maximum Pain

Briefly, maximum pain is the stock price at which the maximum number of contracts on the options chain go out of the money. Max pain has been discussed extensively on this sub for a long time, and the traditional dogma is that the market makers, or the options sellers, are manipulating the price of the stock to always end at max pain, the price at which the most number of options buyers end up with worthless contracts. The conclusion of this statement is that buying options is simply giving money to the opposition and doing nothing to furthering MOASS (potentially even hurting MOASS!). My hope is that by the end of this DD many people who feel this way will at least reconsider and challenge this sentiment.

Historical Max Pain for GME

Below is the historical max pain price plotted alongside the price of GME. I don’t even need to do a regression to prove to you that they are correlated (R^2 = 0.7278). The most notable deviation is during the January Sneeze, mainly because the price exceeded the maximum strike on the chain and it took a few days to expand the chain strikes. Otherwise throughout the rest of the year, they tracked quite closely. However, we all know correlation does not by itself show causation, so lets analyze the data a bit further.

r/Superstonk - Max Pain: A Story of a Dog and his Tail

GME stock price and max pain over time.

Cross Correlation

A cross correlation attempts to find the similarity between two signals. One useful purpose of the cross correlation is to find the time delay between two signals. You can read more about them here.

https://en.wikipedia.org/wiki/Cross-correlation

Let’s see what the cross correlation looks like between the price of GME and max pain.

r/Superstonk - Max Pain: A Story of a Dog and his Tail

Cross correlation between GME stock price and max pain, showing that max pain LAGS GME price by a few days.

Interestingly, the cross correlation shows that max pain LAGS the price of GME by a few days. This is not a smoking gun by itself, but it does indicate that max pain may not be driving the price of the stock, but rather it follows the price of the stock. If market makers were intentionally pushing the price to max pain, then max pain should lead the price of the stock, not lag.

Evolution of Max Pain by Expiry

Now let’s do a deeper dive into how the max pain of each options expiry evolves over time. The figure below plots max pain for each expiry sequentially one at a time (I tried a lot of different ways to show them all on the same graph but they were all pretty hard to follow). The max pain of each individual options chain expiry varies quite dramatically over its entire life.

Evolution of max pain over time, where each frame in the animation is a single expiry.

As can be seen here, essentially every option expiry data has a max pain price that moves dramatically over time. How does the variance of the max pain price over time compare to the variance of the price of GME over time? See the graph below which compares the variance of both.

r/Superstonk - Max Pain: A Story of a Dog and his Tail

Variance of GME stock price vs. the variance of Max pain for all expiries over time.

It seems that the amount that max pain shifts over time is directly correlated to the amount that the price of GME shifts over time. In fact, over all expiries for the last year, the variance of max pain has been about 74.1% (not joking) of the variance of the GME stock price. If the market makers selling options are in control of the price, why is max pain constantly fluctuating with the price?

GME Price vs. Relative Delta Strength

Okay, so the dog has been spinning in circles, is it dog chases tail, or tail chases dog? To get more insight into whether max pain drives the price or the price drives max pain, we need to dig deeper into how options can modify the price of the underlying stock. I go into the evidence that hedging options drives the price of the underlying stock in my previous DDs listed at the top. I encourage you to go read them if you have not, as I am going to use some of the concepts built there to make arguments here. Most importantly is the concept of the relative delta strength (RDS), which is essentially just a normalized measure of the call to put delta on the options chain. A value of 1 is all call delta, a value of -1 is all put delta, and a value of 0 is equal call and put delta. In my previous posts I showed graphically that: 1) option delta and GME price are very well correlated, and 2) changes in options delta appear to precede changes in price. Given these two observations, it is reasonable to believe that hedging option delta drives the price in a stock that is otherwise held by apes and not being traded.

Here I provide further evidence that changes in option delta PRECEDE changes in GME price. Below is a graph of the cross correlation between the RDS and GME price, showing that RDS leads GME price by a few days.

r/Superstonk - Max Pain: A Story of a Dog and his Tail

Cross correlation between GME price and the Relative Delta Strength (RDS). Here, RDS precedes the price of GME by a few days.

What the hell is going on here? First GME options delta shifts, then GME price shifts, and then GME max pain shifts? How could this make any sense if market makers are manipulating the price of GME to close at max pain? If they were manipulating the stock price directly to close at max pain then one would expect max pain to precede GME price. It does not. Manipulating the options chain without hedging using the underlying would expose them to risks that their business model was not designed to bear, and which my previous posts showed has only happened a few times early on in the GME saga.

Okay, so if they are largely hedging the options they sell, what is the explanation? The data I am presenting here is consistent with the data I have been presenting about the options chain previously. Specifically, the price of GME is largely being dictated by options hedging, and a natural consequence of this fact is that max pain will FOLLOW the price of GME. We have all been listening to the line “don’t buy options, the market makers are manipulating the price and we always just end at max pain anyway.” In reality, the options drive the price and drive max pain.

Conclusion

Based on the totality of the data I have analyzed in the current and previous DD’s, it appears that options are largely driving the price of GME. As a consequence, max pain FOLLOWS the price, and does NOT dictate the price.

Then we all should go out and buy options, right? Hell no. At this point I don’t want a single person reading this to buy an option. The amount of hate that has poured out onto those of us that are just trying to understand how options are being used to manipulate the price has been torrential. Every time someone on Superstonk buys an option, an anti-options shill gets an erection. Options are complicated, risky, and expensive, and if you buy an option you will lose all of your money. I simply want the community to understand what is happening with their investment, and how shorts are manipulating the price using options. At the end of the day, we are all individual investors and we will make our own decisions.

Please, please, please, do not give erections to the anti-options commenters below by purchasing options.

DO please comment with your interesting options questions. As mentioned above, this post was motivated by a lot of questions I received about max pain on my previous posts, and I hope I delivered for those folks. It’s okay if you got erections.

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Special Thank you to u/gherkinit and all of the folks he helped bring together to study GME. Without them I would not have the data I presented here, nor the knowledge of the market to interpret it.

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