Black Scholes Option Pricing Model Definition, Example
Black-Scholes Valuaion for Binary Options Trading - Binary ...
No gods, no kings, only NOPE - or divining the future with options flows. [Part 2: A Random Walk and Price Decoherence]
tl;dr - 1) Stock prices move continuously because different market participants end up having different ideas of the future value of a stock. 2) This difference in valuations is part of the reason we have volatility. 3) IV crush happens as a consequence of future possibilities being extinguished at a binary catalyst like earnings very rapidly, as opposed to the normal slow way. I promise I'm getting to the good parts, but I'm also writing these as a guidebook which I can use later so people never have to talk to me again. In this part I'm going to start veering a bit into the speculation territory (e.g. ideas I believe or have investigated, but aren't necessary well known) but I'm going to make sure those sections are properly marked as speculative (and you can feel free to ignore/dismiss them). Marked as [Lily's Speculation]. As some commenters have pointed out in prior posts, I do not have formal training in mathematical finance/finance (my background is computer science, discrete math, and biology), so often times I may use terms that I've invented which have analogous/existing terms (e.g. the law of surprise is actually the first law of asset pricing applied to derivatives under risk neutral measure, but I didn't know that until I read the papers later). If I mention something wrong, please do feel free to either PM me (not chat) or post a comment, and we can discuss/I can correct it! As always, buyer beware. This is the first section also where you do need to be familiar with the topics I've previously discussed, which I'll add links to shortly (my previous posts: 1) https://www.reddit.com/thecorporation/comments/jck2q6/no_gods_no_kings_only_nope_or_divining_the_future/ 2) https://www.reddit.com/thecorporation/comments/jbzzq4/why_options_trading_sucks_or_the_law_of_surprise/ --- A Random Walk Down Bankruptcy A lot of us have probably seen the term random walk, maybe in the context of A Random Walk Down Wall Street, which seems like a great book I'll add to my list of things to read once I figure out how to control my ADD. It seems obvious, then, what a random walk means - when something is moving, it basically means that the next move is random. So if my stock price is $1 and I can move in $0.01 increments, if the stock price is truly randomly walking, there should be roughly a 50% chance it moves up in the next second (to $1.01) or down (to $0.99). If you've traded for more than a hot minute, this concept should seem obvious, because especially on the intraday, it usually isn't clear why price moves the way it does (despite what chartists want to believe, and I'm sure a ton of people in the comments will tell me why fettucini lines and Batman doji tell them things). For a simple example, we can look at SPY's chart from Friday, Oct 16, 2020: https://preview.redd.it/jgg3kup9dpt51.png?width=1368&format=png&auto=webp&s=bf8e08402ccef20832c96203126b60c23277ccc2 I'm sure again 7 different people can tell me 7 different things about why the chart shape looks the way it does, or how if I delve deeply enough into it I can find out which man I'm going to marry in 2024, but to a rationalist it isn't exactly apparent at why SPY's price declined from 349 to ~348.5 at around 12:30 PM, or why it picked up until about 3 PM and then went into precipitous decline (although I do have theories why it declined EOD, but that's for another post). An extremely clever or bored reader from my previous posts could say, "Is this the price formation you mentioned in the law of surprise post?" and the answer is yes. If we relate it back to the individual buyer or seller, we can explain the concept of a stock price's random walk as such:
Most market participants have an idea of an asset's truevalue (an idealized concept of what an asset is actually worth), which they can derive using models or possibly enough brain damage. However, an asset's value at any given time is not worth one value (usually*), but a spectrum of possible values, usually representing what the asset should be worth in the future. A naive way we can represent this without delving into to much math (because let's face it, most of us fucking hate math) is: Current value of an asset = sum over all (future possible value multiplied by the likelihood of that value)
In actuality, most models aren't that simple, but it does generalize to a ton of more complicated models which you need more than 7th grade math to understand (Black-Scholes, DCF, blah blah blah). While in many cases the first term - future possible value - is well defined (Tesla is worth exactly $420.69 billion in 2021, and maybe we all can agree on that by looking at car sales and Musk tweets), where it gets more interesting is the second term - the likelihood of that value occurring. [In actuality, the price of a stock for instance is way more complicated, because a stock can be sold at any point in the future (versus in my example, just the value in 2021), and needs to account for all values of Tesla at any given point in the future.] How do we estimate the second term - the likelihood of that value occurring? For this class, it actually doesn't matter, because the key concept is this idea: even with all market participants having the same information, we do anticipate that every participant will have a slightly different view of future likelihoods. Why is that? There's many reasons. Some participants may undervalue risk (aka WSB FD/yolos) and therefore weight probabilities of gaining lots of money much more heavily than going bankrupt. Some participants may have alternative data which improves their understanding of what the future values should be, therefore letting them see opportunity. Some participants might overvalue liquidity, and just want to GTFO and thereby accept a haircut on their asset's value to quickly unload it (especially in markets with low liquidity). Some participants may just be yoloing and not even know what Fastly does before putting their account all in weekly puts (god bless you). In the end, it doesn't matter either the why, but the what: because of these diverging interpretations, over time, we can expect the price of an asset to drift from the current value even with no new information added. In most cases, the calculations that market participants use (which I will, as a Lily-ism, call the future expected payoff function, or FEPF) ends up being quite similar in aggregate, and this is why asset prices likely tend to move slightly up and down for no reason (or rather, this is one interpretation of why). At this point, I expect the 20% of you who know what I'm talking about or have a finance background to say, "Oh but blah blah efficient market hypothesis contradicts random walk blah blah blah" and you're correct, but it also legitimately doesn't matter here. In the long run, stock prices are clearly not a random walk, because a stock's value is obviously tied to the company's fundamentals (knock on wood I don't regret saying this in the 2020s). However, intraday, in the absence of new, public information, it becomes a close enough approximation. Also, some of you might wonder what happens when the future expected payoff function (FEPF) I mentioned before ends up wildly diverging for a stock between participants. This could happen because all of us try to short Nikola because it's quite obviously a joke (so our FEPF for Nikola could, let's say, be 0), while the 20 or so remaining bagholders at NikolaCorporation decide that their FEPF of Nikola is $10,000,000 a share). One of the interesting things which intuitively makes sense, is for nearly all stocks, the amount of divergence among market participants in their FEPF increases substantially as you get farther into the future. This intuitively makes sense, even if you've already quit trying to understand what I'm saying. It's quite easy to say, if at 12:51 PM SPY is worth 350.21 that likely at 12:52 PM SPY will be worth 350.10 or 350.30 in all likelihood. Obviously there are cases this doesn't hold, but more likely than not, prices tend to follow each other, and don't gap up/down hard intraday. However, what if I asked you - given SPY is worth 350.21 at 12:51 PM today, what will it be worth in 2022? Many people will then try to half ass some DD about interest rates and Trump fleeing to Ecuador to value SPY at 150, while others will assume bull markets will continue indefinitely and SPY will obviously be 7000 by then. The truth is -- no one actually knows, because if you did, you wouldn't be reading a reddit post on this at 2 AM in your jammies. In fact, if you could somehow figure out the FEPF of all market participants at any given time, assuming no new information occurs, you should be able to roughly predict the true value of an asset infinitely far into the future (hint: this doesn't exactly hold, but again don't @ me). Now if you do have a finance background, I expect gears will have clicked for some of you, and you may see strong analogies between the FEPF divergence I mentioned, and a concept we're all at least partially familiar with - volatility. Volatility and Price Decoherence ("IV Crush") Volatility, just like the Greeks, isn't exactly a real thing. Most of us have some familiarity with implied volatility on options, mostly when we get IV crushed the first time and realize we just lost $3000 on Tesla calls. If we assume that the current price should represent the weighted likelihoods of all future prices (the random walk), volatility implies the following two things:
Volatility reflects the uncertainty of the current price
Volatility reflects the uncertainty of the future price for every point in the future where the asset has value (up to expiry for options)
[Ignore this section if you aren't pedantic] There's obviously more complex mathematics, because I'm sure some of you will argue in the comments that IV doesn't go up monotonically as option expiry date goes longer and longer into the future, and you're correct (this is because asset pricing reflects drift rate and other factors, as well as certain assets like the VIX end up having cost of carry). Volatility in options is interesting as well, because in actuality, it isn't something that can be exactly computed -- it arises as a plug between the idealized value of an option (the modeled price) and the real, market value of an option (the spot price). Additionally, because the makeup of market participants in an asset's market changes over time, and new information also comes in (thereby increasing likelihood of some possibilities and reducing it for others), volatility does not remain constant over time, either. Conceptually, volatility also is pretty easy to understand. But what about our friend, IV crush? I'm sure some of you have bought options to play events, the most common one being earnings reports, which happen quarterly for every company due to regulations. For the more savvy, you might know of expected move, which is a calculation that uses the volatility (and therefore price) increase of at-the-money options about a month out to calculate how much the options market forecasts the underlying stock price to move as a response to ER. Binary Catalyst Events and Price Decoherence Remember what I said about price formation being a gradual, continuous process? In the face of special circumstances, in particularly binary catalyst events - events where the outcome is one of two choices, good (1) or bad (0) - the gradual part gets thrown out the window. Earnings in particular is a common and notable case of a binary event, because the price will go down (assuming the company did not meet the market's expectations) or up (assuming the company exceeded the market's expectations) (it will rarely stay flat, so I'm not going to address that case). Earnings especially is interesting, because unlike other catalytic events, they're pre-scheduled (so the whole market expects them at a certain date/time) and usually have publicly released pre-estimations (guidance, analyst predictions). This separates them from other binary catalysts (e.g. FSLY dipping 30% on guidance update) because the market has ample time to anticipate the event, and participants therefore have time to speculate and hedge on the event. In most binary catalyst events, we see rapid fluctuations in price, usually called a gap up or gap down, which is caused by participants rapidly intaking new information and changing their FEPF accordingly. This is for the most part an anticipated adjustment to the FEPF based on the expectation that earnings is a Very Big Deal (TM), and is the reason why volatility and therefore option premiums increase so dramatically before earnings. What makes earnings so interesting in particular is the dramatic effect it can have on all market participants FEPF, as opposed to let's say a Trump tweet, or more people dying of coronavirus. In lots of cases, especially the FEPF of the short term (3-6 months) rapidly changes in response to updated guidance about a company, causing large portions of the future possibility spectrum to rapidly and spectacularly go to zero. In an instant, your Tesla 10/30 800Cs go from "some value" to "not worth the electrons they're printed on". [Lily's Speculation] This phenomena, I like to call price decoherence, mostly as an analogy to quantum mechanical processes which produce similar results (the collapse of a wavefunction on observation). Price decoherence occurs at a widespread but minor scale continuously, which we normally call price formation (and explains portions of the random walk derivation explained above), but hits a special limit in the face of binary catalyst events, as in an instant rapid portions of the future expected payoff function are extinguished, versus a more gradual process which occurs over time (as an option nears expiration). Price decoherence, mathematically, ends up being a more generalizable case of the phenomenon we all love to hate - IV crush. Price decoherence during earnings collapses the future expected payoff function of a ticker, leading large portions of the option chain to be effectively worthless (IV crush). It has interesting implications, especially in the case of hedged option sellers, our dear Market Makers. This is because given the expectation that they maintain delta-gamma neutral, and now many of the options they have written are now worthless and have 0 delta, what do they now have to do? They have to unwind. [/Lily's Speculation] - Lily
No gods, no kings, only NOPE - or divining the future with options flows. [Part 3: Hedge Winding, Unwinding, and the NOPE]
Hello friends! We're on the last post of this series ("A Gentle Introduction to NOPE"), where we get to use all the Big Boy Concepts (TM) we've discussed in the prior posts and put them all together. Some words before we begin:
This post will be massively theoretical, in the sense that my own speculation and inferences will be largely peppered throughout the post. Are those speculations right? I think so, or I wouldn't be posting it, but they could also be incorrect.
I will briefly touch on using the NOPE this slide, but I will make a secondary post with much more interesting data and trends I've observed. This is primarily for explaining what NOPE is and why it potentially works, and what it potentially measures.
My advice before reading this is to glance at my prior posts, and either read those fully or at least make sure you understand the tl;drs: https://www.reddit.com/thecorporation/collection/27dc72ad-4e78-44cd-a788-811cd666e32a Depending on popular demand, I will also make a last-last post called FAQ, where I'll tabulate interesting questions you guys ask me in the comments! --- So a brief recap before we begin. Market Maker ("Mr. MM"): An individual or firm who makes money off the exchange fees and bid-ask spread for an asset, while usually trying to stay neutral about the direction the asset moves. Delta-gamma hedging: The process Mr. MM uses to stay neutral when selling you shitty OTM options, by buying/selling shares (usually) of the underlying as the price moves. Law of Surprise [Lily-ism]: Effectively, the expected profit of an options trade is zero for both the seller and the buyer. Random Walk: A special case of a deeper probability probability called a martingale, which basically models stocks or similar phenomena randomly moving every step they take (for stocks, roughly every millisecond). This is one of the most popular views of how stock prices move, especially on short timescales. Future Expected Payoff Function [Lily-ism]: This is some hidden function that every market participant has about an asset, which more or less models all the possible future probabilities/values of the assets to arrive at a "fair market price". This is a more generalized case of a pricing model like Black-Scholes, or DCF. Counter-party: The opposite side of your trade (if you sell an option, they buy it; if you buy an option, they sell it). Price decoherence ]Lily-ism]: A more generalized notion of IV Crush, price decoherence happens when instead of the FEPF changing gradually over time (price formation), the FEPF rapidly changes, due usually to new information being added to the system (e.g. Vermin Supreme winning the 2020 election). --- One of the most popular gambling events for option traders to play is earnings announcements, and I do owe the concept of NOPE to hypothesizing specifically about the behavior of stock prices at earnings. Much like a black hole in quantum mechanics, most conventional theories about how price should work rapidly break down briefly before, during, and after ER, and generally experienced traders tend to shy away from playing earnings, given their similar unpredictability. Before we start: what is NOPE? NOPE is a funny backronym from Net Options Pricing Effect, which in its most basic sense, measures the impact option delta has on the underlying price, as compared to share price. When I first started investigating NOPE, I called it OPE (options pricing effect), but NOPE sounds funnier. The formula for it is dead simple, but I also have no idea how to do LaTeX on reddit, so this is the best I have: https://preview.redd.it/ais37icfkwt51.png?width=826&format=png&auto=webp&s=3feb6960f15a336fa678e945d93b399a8e59bb49 Since I've already encountered this, put delta in this case is the absolute value (50 delta) to represent a put. If you represent put delta as a negative (the conventional way), do not subtract it; add it. To keep this simple for the non-mathematically minded: the NOPE today is equal to the weighted sum (weighted by volume) of the delta of every call minus the delta of every put for all options chains extending from today to infinity. Finally, we then divide that number by the # of shares traded today in the market session (ignoring pre-market and post-market, since options cannot trade during those times). Effectively, NOPE is a rough and dirty way to approximate the impact of delta-gamma hedging as a function of share volume, with us hand-waving the following factors:
To keep calculations simple, we assume that all counter-parties are hedged. This is obviously not true, especially for idiots who believe theta ganging is safe, but holds largely true especially for highly liquid tickers, or tickers will designated market makers (e.g. any ticker in the NASDAQ, for instance).
We assume that all hedging takes place via shares. For SPY and other products tracking the S&P, for instance, market makers can actually hedge via futures or other options. This has the benefit for large positions of not moving the underlying price, but still makes up a fairly small amount of hedges compared to shares.
Winding and Unwinding
I briefly touched on this in a past post, but two properties of NOPE seem to apply well to EER-like behavior (aka any binary catalyst event):
NOPE measures sentiment - In general, the options market is seen as better informed than share traders (e.g. insiders trade via options, because of leverage + easier to mask positions). Therefore, a heavy call/put skew is usually seen as a bullish sign, while the reverse is also true.
NOPE measures system stability
I'm not going to one-sentence explain #2, because why say in one sentence what I can write 1000 words on. In short, NOPE intends to measure sensitivity of the system (the ticker) to disruption. This makes sense, when you view it in the context of delta-gamma hedging. When we assume all counter-parties are hedged, this means an absolutely massive amount of shares get sold/purchased when the underlying price moves. This is because of the following: a) Assume I, Mr. MM sell 1000 call options for NKLA 25C 10/23 and 300 put options for NKLA 15p 10/23. I'm just going to make up deltas because it's too much effort to calculate them - 30 delta call, 20 delta put. This implies Mr. MM needs the following to delta hedge: (1000 call options * 30 shares to buy for each) [to balance out writing calls) - (300 put options * 20 shares to sell for each) = 24,000net shares Mr. MM needs to acquire to balance out his deltas/be fully neutral. b) This works well when NKLA is at $20. But what about when it hits $19 (because it only can go down, just like their trucks). Thanks to gamma, now we have to recompute the deltas, because they've changed for both the calls (they went down) and for the puts (they went up). Let's say to keep it simple that now my calls are 20 delta, and my puts are 30 delta. From the 24,000 net shares, Mr. MM has to now have: (1000 call options * 20 shares to have for each) - (300 put options * 30 shares to sell for each) = 11,000 shares. Therefore, with a $1 shift in price, now to hedge and be indifferent to direction, Mr. MM has to go from 24,000 shares to 11,000 shares, meaning he has to sell 13,000 shares ASAP, or take on increased risk. Now, you might be saying, "13,000 shares seems small. How would this disrupt the system?" (This process, by the way, is called hedge unwinding) It won't, in this example. But across thousands of MMs and millions of contracts, this can - especially in highly optioned tickers - make up a substantial fraction of the net flow of shares per day. And as we know from our desk example, the buying or selling of shares directly changes the price of the stock itself. This, by the way, is why the NOPE formula takes the shape it does. Some astute readers might notice it looks similar to GEX, which is not a coincidence. GEX however replaces daily volume with open interest, and measures gamma over delta, which I did not find good statistical evidence to support, especially for earnings. So, with our example above, why does NOPE measure system stability? We can assume for argument's sake that if someone buys a share of NKLA, they're fine with moderate price swings (+- $20 since it's NKLA, obviously), and in it for the long/medium haul. And in most cases this is fine - we can own stock and not worry about minor swings in price. But market makers can't* (they can, but it exposes them to risk), because of how delta works. In fact, for most institutional market makers, they have clearly defined delta limits by end of day, and even small price changes require them to rebalance their hedges. This over the whole market adds up to a lot shares moving, just to balance out your stupid Robinhood YOLOs. While there are some tricks (dark pools, block trades) to not impact the price of the underlying, the reality is that the more options contracts there are on a ticker, the more outsized influence it will have on the ticker's price. This can technically be exactly balanced, if option put delta is equal to option call delta, but never actually ends up being the case. And unlike shares traded, the shares representing the options are more unstable, meaning they will be sold/bought in response to small price shifts. And will end up magnifying those price shifts, accordingly.
NOPE and Earnings
So we have a new shiny indicator, NOPE. What does it actually mean and do? There's much literature going back to the 1980s that options markets do have some level of predictiveness towards earnings, which makes sense intuitively. Unlike shares markets, where you can continue to hold your share even if it dips 5%, in options you get access to expanded opportunity to make riches... and losses. An options trader betting on earnings is making a risky and therefore informed bet that he or she knows the outcome, versus a share trader who might be comfortable bagholding in the worst case scenario. As I've mentioned largely in comments on my prior posts, earnings is a special case because, unlike popular misconceptions, stocks do not go up and down solely due to analyst expectations being meet, beat, or missed. In fact, stock prices move according to the consensus market expectation, which is a function of all the participants' FEPF on that ticker. This is why the price moves so dramatically - even if a stock beats, it might not beat enough to justify the high price tag (FSLY); even if a stock misses, it might have spectacular guidance or maybe the market just was assuming it would go bankrupt instead. To look at the impact of NOPE and why it may play a role in post-earnings-announcement immediate price moves, let's review the following cases:
Stock Meets/Exceeds Market Expectations (aka price goes up) - In the general case, we would anticipate post-ER market participants value the stock at a higher price, pushing it up rapidly. If there's a high absolute value of NOPE on said ticker, this should end up magnifying the positive move since:
a) If NOPE is high negative - This means a ton of put buying, which means a lot of those puts are now worthless (due to price decoherence). This means that to stay delta neutral, market makers need to close out their sold/shorted shares, buying them, and pushing the stock price up. b) If NOPE is high positive - This means a ton of call buying, which means a lot of puts are now worthless (see a) but also a lot of calls are now worth more. This means that to stay delta neutral, market makers need to close out their sold/shorted shares AND also buy more shares to cover their calls, pushing the stock price up. 2) Stock Meets/Misses Market Expectations (aka price goes down)- Inversely to what I mentioned above, this should push to the stock price down, fairly immediately. If there's a high absolute value of NOPE on said ticker, this should end up magnifying the negative move since: a) If NOPE is high negative - This means a ton of put buying, which means a lot of those puts are now worth more, and a lot of calls are now worth less/worth less (due to price decoherence). This means that to stay delta neutral, market makers need to sell/short more shares, pushing the stock price down. b) If NOPE is high positive - This means a ton of call buying, which means a lot of calls are now worthless (see a) but also a lot of puts are now worth more. This means that to stay delta neutral, market makers need to sell even more shares to keep their calls and puts neutral, pushing the stock price down. --- Based on the above two cases, it should be a bit more clear why NOPE is a measure of sensitivity to system perturbation. While we previously discussed it in the context of magnifying directional move, the truth is it also provides a directional bias to our "random" walk. This is because given a price move in the direction predicted by NOPE, we expect it to be magnified, especially in situations of price decoherence. If a stock price goes up right after an ER report drops, even based on one participant deciding to value the stock higher, this provides a runaway reaction which boosts the stock price (due to hedging factors as well as other participants' behavior) and inures it to drops.
NOPE and NOPE_MAD
I'm going to gloss over this section because this is more statistical methods than anything interesting. In general, if you have enough data, I recommend using NOPE_MAD over NOPE. While NOPE in theory represents a "real" quantity (net option delta over net share delta), NOPE_MAD (the median absolute deviation of NOPE) does not. NOPE_MAD simply answecompare the following:
How exceptional is today's NOPE versus historic baseline (30 days prior)?
How do I compare two tickers' NOPEs effectively (since some tickers, like TSLA, have a baseline positive NOPE, because Elon memes)? In the initial stages, we used just a straight numerical threshold (let's say NOPE >= 20), but that quickly broke down. NOPE_MAD aims to detect anomalies, because anomalies in general give you tendies.
I might add the formula later in Mathenese, but simply put, to find NOPE_MAD you do the following:
Calculate today's NOPE score (this can be done end of day or intraday, with the true value being EOD of course)
Calculate the end of day NOPE scores on the ticker for the previous 30 trading days
Compute the median of the previous 30 trading days' NOPEs
Find today's deviation as compared to the MAD calculated by: [(today's NOPE) - (median NOPE of last 30 days)] / (median absolute deviation of last 30 days)
This is usually reported as sigma (σ), and has a few interesting properties:
The mean of NOPE_MAD for any ticker is almost exactly 0.
[Lily's Speculation's Speculation] NOPE_MAD acts like a spring, and has a tendency to reverse direction as a function of its magnitude. No proof on this yet, but exploring it!
Using the NOPE to predict ER
So the last section was a lot of words and theory, and a lot of what I'm mentioning here is empirically derived (aka I've tested it out, versus just blabbered). In general, the following holds true:
3 sigma NOPE_MAD tends to be "the threshold": For very low NOPE_MAD magnitudes (+- 1 sigma), it's effectively just noise, and directionality prediction is low, if not non-existent. It's not exactly like 3 sigma is a play and 2.9 sigma is not a play; NOPE_MAD accuracy increases as NOPE_MAD magnitude (either positive or negative) increases.
NOPE_MAD is only useful on highly optioned tickers: In general, I introduce another parameter for sifting through "candidate" ERs to play: option volume * 100/share volume. When this ends up over let's say 0.4, NOPE_MAD provides a fairly good window into predicting earnings behavior.
NOPE_MAD only predicts during the after-market/pre-market session: I also have no idea if this is true, but my hunch is that next day behavior is mostly random and driven by market movement versus earnings behavior. NOPE_MAD for now only predicts direction of price movements right between the release of the ER report (AH or PM) and the ending of that market session. This is why in general I recommend playing shares, not options for ER (since you can sell during the AH/PM).
NOPE_MAD only predicts direction of price movement: This isn't exactly true, but it's all I feel comfortable stating given the data I have. On observation of ~2700 data points of ER-ticker events since Mar 2019 (SPY 500), I only so far feel comfortable predicting whether stock price goes up (>0 percent difference) or down (<0 price difference). This is +1 for why I usually play with shares.
Some statistics: #0) As a baseline/null hypothesis, after ER on the SPY500 since Mar 2019, 50-51% price movements in the AH/PM are positive (>0) and ~46-47% are negative (<0). #1) For NOPE_MAD >= +3 sigma, roughly 68% of price movements are positive after earnings. #2) For NOPE_MAD <= -3 sigma, roughly 29% of price movements are positive after earnings. #3) When using a logistic model of only data including NOPE_MAD >= +3 sigma or NOPE_MAD <= -3 sigma, and option/share vol >= 0.4 (around 25% of all ERs observed), I was able to achieve 78% predictive accuracy on direction.
Like all models, NOPE is wrong, but perhaps useful. It's also fairly new (I started working on it around early August 2020), and in fact, my initial hypothesis was exactly incorrect (I thought the opposite would happen, actually). Similarly, as commenters have pointed out, the timeline of data I'm using is fairly compressed (since Mar 2019), and trends and models do change. In fact, I've noticed significantly lower accuracy since the coronavirus recession (when I measured it in early September), but I attribute this mostly to a smaller date range, more market volatility, and honestly, dumber option traders (~65% accuracy versus nearly 80%). My advice so far if you do play ER with the NOPE method is to use it as following:
Buy/short shares approximately right when the market closes before ER. Ideally even buying it right before the earnings report drops in the AH session is not a bad idea if you can.
Sell/buy to close said shares at the first sign of major weakness (e.g. if the NOPE predicted outcome is incorrect).
Sell/buy to close shares even if it is correct ideally before conference call, or by the end of the after-market/pre-market session.
Only play tickers with high NOPE as well as high option/share vol.
--- In my next post, which may be in a few days, I'll talk about potential use cases for SPY and intraday trends, but I wanted to make sure this wasn't like 7000 words by itself. Cheers. - Lily
Selling your Covered Call - Thoughts on How to Select Your Strike and Expiration
Congratulations! You are a bag holder of company XYZ which was thought to be the best penny stock ever. Instead of feeling sorry, you consider selling covered calls to help reduce your cost basis - and eventually get out of your bags with minimal loss or even a profit! First - let's review the call option contract. The holder of the call option contract has the right but not the obligation to purchase 100 shares of XYZ at the strike price per share. This contract has an expiration date. We assume American style option contracts which means that the option can be exercised at any point prior to expiration. Thus, there are three parameters to the option contract - the strike price, the expiration date and the premium - which represents the price per share of the contract. The holder of the call option contract is the person that buys the option. The writer of the contract is the seller. The buyer (or holder) pays the premium. The seller (or writer) collects the premium. As an XYZ bag holder, the covered call may help. By writing a call contract against your XYZ shares, you can collect premium to reduce your investment cost in XYZ - reducing your average cost per share. For every 100 shares of XYZ, you can write 1 call contract. Notice that that by selling the contract, you do not control if the call is exercised - only the holder of the contract can exercise it. There are several online descriptions about the covered call strategy. Here is an example that might be useful to review Covered Call Description The general guidance is to select the call strike at the price in which you would be happy selling your shares. However, the context of most online resources on the covered call strategy assume that you either just purchased the shares at market value or your average cost is below the market price. In the case as a bag holder, your average cost is most likely over - if not significantly over - the current market price. This situation simply means that you have a little work to reduce your average before you are ready to have your bags called away. For example, you would not want to have your strike set at $2.50 when your average is above that value as this would guarantee a net loss. (However, if you are simply trying to rid your bags and your average is slightly above the strike, then you might consider it as the strike price). One more abstract concept before getting to what you want to know. The following link shows the Profit/Loss Diagram for Covered Call Conceptually, the blue line shows the profit/loss value of your long stock position. The line crosses the x-axis at your average cost, i.e the break-even point for the long stock position. The green/red hockey stick is the profit (green) or loss (red) of the covered call position (100 long stock + 1 short call option). The profit has a maximum value at the strike price. This plateau is due to the fact that you only receive the agreed upon strike price per share when the call option is exercised. Below the strike, the profit decreases along the unit slope line until the value becomes negative. It is a misnomer to say that the covered call is at 'loss' since it is really the long stock that has decreased in value - but it is not loss (yet). Note that the break-even point marked in the plot is simply the reduced averaged cost from the collected premium selling the covered call. As a bag holder, it will be a two-stage process: (1) reduce the average cost (2) get rid of bags. Okay let's talk selecting strike and expiration. You must jointly select these two parameters. Far OTM strikes will collect less premium where the premium will increase as you move the strike closer to the share price. Shorter DTE will also collect less premium where the premium will increase as you increase the DTE. It is easier to describe stage 2 "get rid of bags" first. Let us pretend that our hypothetical bag of 100 XYZ shares cost us $5.15/share. The current XYZ market price is $3/share - our hole is $2.15/share that we need to dig out. Finally, assume the following option chain (all hypothetical):
Purely made up the numbers, but the table illustrates the notional behavior of an option chain. The option value (premium) is the intrinsic value plus the time value. Only the $2.5 strike has intrinsic value since the share price is $3 (which is greater than $2.5). Notice that intrinsic value cannot be negative. The rest of the premium is the time value of the option which is essentially the monetary bet associated with the probability that the share price will exceed the strike at expiration. According to the table, we could collect the most premium by selling the 110 DTE $2.5 call for $0.95. However, there is a couple problems with that option contract. We are sitting with bags at $5.15/share and receiving $0.95 will only reduce our average to $4.20/share. On expiration, if still above $2.5, then we are assigned, shares called away and we receive $2.50/share or a loss of $170 - not good. Well, then how about the $5 strike at 110 DTE for $0.50? This reduces us to $4.65/share which is under the $5 strike so we would make a profit of $35! This is true - however 110 days is a long time to make $35. You might say that is fine you just want to get the bags gone don't care. Well maybe consider a shorter DTE - even the 20 DTE or 50 DTE would collect premium that reduces your average below $5. This would allow you to react to any stock movement that occurs in the near-term. Consider person A sells the 110 DTE $5 call and person B sells the 50 DTE $5 call. Suppose that the XYZ stock increases to $4.95/share in 50 days then goes to $8 in the next 30 days then drops to $3 after another 30 days. This timeline goes 110 days and person A had to watch the price go up and fall back to the same spot with XYZ stock at $3/share. Granted the premium collected reduced the average but stilling hold the bags. Person B on the other hand has the call expire worthless when XYZ is at $4.95/share. A decision can be made - sell immediately, sell another $5 call or sell a $7.5 call. Suppose the $7.5 call is sold with 30 DTE collecting some premium, then - jackpot - the shares are called away when XYZ is trading at $8/share! Of course, no one can predict the future, but the shorter DTE enables more decision points. The takeaway for the second step in the 2-stage approach is that you need to select your profit target to help guide your strike selection. In this example, are you happy with the XYZ shares called away at $5/share or do you want $7.5/share? What is your opinion on the stock price trajectory? When do you foresee decision points? This will help determine the strike/expiration that matches your thoughts. Note: studies have shown that actively managing your position results in better performance than simply waiting for expiration, so you can adjust the position if your assessment on the movement is incorrect. Let's circle back to the first step "reduce the average cost". What if your average cost of your 100 shares of XYZ is $8/share? Clearly, all of the strikes in our example option chain above is "bad" to a certain extent since we would stand to lose a lot of money if the option contract is exercised. However, by describing the second step, we know the objective for this first step is to reduce our average such that we can profit from the strikes. How do we achieve this objective? It is somewhat the same process as previously described, but you need to do your homework a little more diligently. What is your forecast on the stock movement? Since $7.5 is the closest strike to your average, when do you expect XYZ to rise from $3/share to $7.5/share? Without PR, you might say never. With some PR then maybe 50/50 chance - if so, then what is the outlook for PR? What do you think the chances of going to $5/share where you could collect more premium? Suppose that a few XYZ bag holders (all with a $8/share cost) discuss there outlook of the XYZ stock price in the next 120 days:
Person A does not seem to think much price movement will occur. This person might sell the $5 call with either 20 DTE or 50 DTE. Then upon expiration, sell another $5 call for another 20-50 DTE. Person A could keep repeating this until the average is reduced enough to move onto step-2. Of course, this approach is risky if the Person A price forecast is incorrect and the stock price goes up - which might result in assignment too soon. Person B appears to be the most bullish of the group. This person might sell the $5 call with 20 DTE then upon expiration sell the $7.5 call. After expiration, Person B might decide to leave the shares uncovered because her homework says XYZ is going to explode and she wants to capture those gains! Person C believes that there will be a step increase in 10 days maybe due to major PR event. This person will not have the chance to reduce the average in time to sell quickly, so first he sells a $7.5 call with 20 DTE to chip at the average. At expiration, Person C would continue to sell $7.5 calls until the average at the point where he can move onto the "get rid of bags" step. In all causes, each person must form an opinion on the XYZ price movement. Of course, the prediction will be wrong at some level (otherwise they wouldn't be bag holders!). The takeaway for the first step in the 2-stage approach is that you need to do your homework to better forecast the price movement to identify the correct strikes to bring down your average. The quality of the homework and the risk that you are willing to take will dedicate the speed at which you can reduce your average. Note that if you are unfortunate to have an extremely high average per share, then you might need to consider doing the good old buy-more-shares-to-average-down. This will be the fastest way to reduce your average. If you cannot invest more money, then the approach above will still work, but it will require much more patience. Remember there is no free lunch! Advanced note: there is another method to reduce your (high) average per share - selling cash secured puts. It is the "put version" of a cover call. Suppose that you sell a XYZ $2.5 put contract for $0.50 with 60 DTE. You collect $50 from the premium of the contract. This money is immediately in your bank and reduces your investment cost. But what did you sell? If XYZ is trading below $2.50, then you will be assigned 100 shares of XYZ at $2.50/share or $250. You own more shares, but at a price which will reduce your average further. Being cash secured, your brokerage will reserve $250 from your account when you sell the contract. In essence, you reduce your buying power by $250 and conditionally purchase the shares - you do not have them until assignment. If XYZ is greater than the strike at expiration, then your broker gives back $250 cash / buying power and you keep the premium. Early assignment - one concern is the chance of early assignment. The American style option contract allows the holder the opportunity to exercise the contract at any time prior to expiration. Early assignment almost never occurs. There are special cases that typically deal with dividends but most penny stocks are not in the position to hand out dividends. Aside from that, the holder would be throwing away option time value by early exercise. It possibly can handle - probably won't - it actually would be a benefit when selling covered calls as you would receive your profit more quickly! This post has probably gone too long! I will stop and let's discuss this matter. I will add follow-on material with some of the following topics which factors into this discussion:
Effect of earnings / PR / binary events on the option contract - this reaction may be different than the underlying stock reaction to the event
The Black-Scholes option pricing model allows one to understand how the premium will change - note that "all models are incorrect, but some are useful"
The "Greeks" give you a sense about how prices change when the stock price change - Meet the Greeks video
Position Management - when to adjust, close, or roll
Legging position into strangles/straddles - more advanced position with higher risk / higher reward
Open to other suggestions. I'm sure there are some typos and unclear statements - I will edit as needed! \I'm not a financial advisor. Simply helping to 'coach' people through the process. You are responsible for your decisions. Do not execute a trade that you do not understand. Ask questions if needed!**
Hey all, Still getting used to working on TT and had a question regarding the IVx number listed next to each set of contracts. I've read the TastyWorks definitely of IVx but was hoping somebody could ELI5 it for me. Using AMZN as an example: On Tastytrade it shows an IVx for 2/1 Options Contracts of: 51.3%(+/-115.54) On Schwab (my other broker) they break down Imp Vol. on a strike by strike basis for the contracts expiring 2/1 and each strike has an Imp Vol of <50. Can anyone explain the difference and how I can use it as I become more familiar with how options pricing drives IV?
Hi everybody. Hopefully this post doesn't sound too rant-y but I'm pretty frustrated by the amount of info out there that I'm not able to pick up on. There just seems to be a million ways to do calculated expected move. Here's what I've gathered so far. There seems to be two general methods: First Method: IV-Based
One Standard Deviation Move = (P) (IV) (DTE/365)^0.5
where P = price, IV = annualized implied volatility, DTE = days to expiration  This means that there is a 68% probability that the stock in question will be between -1 and +1 sigma at the date of expiration, a 95% probability between -2 and +2, and a 99% probability between -3 and +3. Sometimes 250-252 is used instead of 365, which seems to be the case when DTE refers to market days until expiration. Is that correct? There are a number of ways to calculate IV. I would appreciate it if somebody could elaborate on which might be best and the differences between them:
ThinkOrSwim uses the Bjerksund-Stensland Model  - I assume this is the "annualized" implied volatility aforementioned, because it is an IV value assigned to the stock as a whole ... what does that mean? I thought IV values were only calculated for a specific option contract??
As an aside, ToS in particular confuses me because none of the IVs seem to correlate - Exhibit A
I thought I might look into how VIX was priced off of SPY , as an analog, and use it as a basis for finding IV for any other stock as a whole. I don't know where they got their formula from
Backsolve for IV using Black-Scholes . This would only gives one value for IV, which I think only applies to that specific option contract and not to the stock as a whole??
Some websites say to use the IV given that is closest to the desired time period  - of course I have no idea how the IV is calculated in the first place (Bjerksund-Stensland again? Black-Scholes?) What's the difference between using the IV of a weekly or a yearly option?
Brenner and Subrahmanyam  - understood that this seems to be just an approximation. Should I be looking at formulas from 1988, however?
A very big question of mine is why there is an implied volatility for the stock as a whole and an implied volatility for every other options contract. I can kind of understand it both ways - why should a later-expiry contract have the same IV as an earlier-expiry contract? On the other hand, why should they be different? Why isn't there just one IV for the stock as a whole? Second Method: Straddle-Based My understanding is that this is more used for binary events like earnings, but in general I've found two methods:
Expected Move = (0.85) (Front Month Straddle)  OR
Expected Move = (Price of Straddle close to Desired Time Period) / (Price of Underlying) 
I have no idea where  comes from and I can sort of understand 6 but not really. In the end, I'm just trying to be as accurate as possible. Is there a best, preferred method to calculating the expected move of a stock in a given timeframe? Is there a best, preferred method to calculating IV (I'm inclined to go with ToS's model simply because they're large and trusted). Is there some Python library out there that already does this? For a retail trader like me, does it even matter?? Any help is appreciated. Thanks!
Hi everyone, I've been working on a project for my Bachelor Thesis in Finance with Python for quite a while now and I'd love to have some feedback from you. The project focuses on Option Pricing using the Black Scholes Model for Plain Vanilla and Binary Options. It allows the user to perform a series of tasks like computing and plotting greeks, option payoffs and the implied volatility surface and skew. The script requires Chrome and quite a few modules to properly work, and the code is macOS native, meaning that it may not work on other operating systems (sorry for that). My go-to IDE is PyCharm, but I guess any other IDE will work fine. Here you can find the link to the GitHub repository where the project is located. I will leave also some links to resources about all the theory behind the computations I do in the project for the ones that are not familiar with this topic. Options Theory) Black-Scholes Model Binary Options Greeks) Options Strategies Implied Volatility Volatility Smile (Skew) If you have any question let me know. Thank you!
Hi all, was doing searching for some research papers like I do every few months, and decided I'd throw them up here if anyone is interested in them. Most of these link directly to pdfs (view, not instant-download). bolded = you should read them If anyone else reads these, I'm sure lots of the guys here would appreciate a quick review, summary points, or just your thoughts on any of them.
Can she squirt? The tale of Taylor Swift and her vibrator (I meant to post this yesterday)
This is how messed up my mind is (and why the title works): Vibrator -> "Good Vibrations" -> The Beach Boys -> "Smile" Album -> Volatility Smile Why Taylor Swift? She is innocent and naive just like most retail. Now that we have that out of the way let's talk options.... So one of things that came out of the 87' crash was what we call the volatility smile which is simply the skew of puts and calls relative to their moniness. So what the fuck does that mean? Prior to the crash a modified black scholes model was used to price options; the problem is that black scholes assumes that volatility is constant - it isn't. When the black swan event occurred vol shot up and everyone lost their asses as both puts and calls were not skewed and thus always under priced. The smile name is derived because the volatility surface resembles a smile or smirk where OTM puts and calls are skewed higher than ATM puts and calls. Here is an example: http://www.optionsideacentral.com/wp-content/uploads/2013/10/AAPL-Skew.gif You can also see the vol skewness on think or swim or ib under the "implied vol" section and see how as you get closer and closer to the ATM vol contracts and then goes up again. the "smirk" (or the look I give a chick after I am caught looking at here clevage) You will see that most smiles are askew to the downside (google volatility smile mother fucker can't do everything for you) - why is this? Isn't it wrong? Max loss to the downside is zero and max loss to the upside is infinity so why is it like this? Volatility on the downside skew is greater than the upside because:
They are insurance of a black swan event
If the skew is noticeably higher then they are getting pounded by buyers
Puts are more expensive to trade
So what brought this lesson on? This question: What's happening with options prices on SPY? looking at sep 26 calls $202 strike. options price was trading higher today when SPY was 200.60 than it is now, when it's 201.21. will things normalize after this volatility? I'm red on my calls when i feel like i should be well in the money Skew is the reason - with a binary event volatility is raised significantly more on the wings (further OTM options) then the ATM (regardless the whole vol surface moves) so when the market doesn't move the skew flattens taking out the higher vol component even though the stock delta may be rising. saavy???
The Option Pricing Model simply cannot overcome the supply and demand curve of option traders hungry for owing a call option on the day of a strong earnings release or a positive press release. The Option Pricing Model was developed by Fischer Black and Myron Scholes in 1973. Myron Scholes - Co-founder of the Black-Scholes Valuation Model for pricing binary option trades. Caricature Portrait of Myron Scholes . Binary options trading has really taken the investment world by storm in recent years. Although conceptualized in the 1970's and 1980's, and the topic of a 1995 Nobel Prize, the real action and volume has only come to fruition in the most recent years. A big ... Black-Scholes binary options strategy is a high/Low strategy that is based on the complex metatrader indicators. This system is applicable to a 5-minutes, 15-minutes, 30-minutes, 60-minutes, 240-minutes, and daily timeframe. This has an expiry time of 5-7 candles. This works on a forex, indices, and commodity market. For timeframes 5 min, 15 min or 30 min trading hours, just trade during the ... The Black-Scholes model was first introduced by Fischer Black and Myron Scholes in 1973 in the paper "The Pricing of Options and Corporate Liabilities". Since being published, the model has become a widely used tool by investors and is still regarded as one of the best ways to determine fair prices of options. The purpose of the model is to determine the price of a vanilla European call and ... If you are not familiar with Black Scholes Options Pricing Formula, you should watch these videos. These videos explain the derivation of Black Scholes formula in simple terms. Watch these videos. In these videos the instructor derives Black Scholes formula mathematically. Once you have understood the mathematical formula and how it is used to calculate the call option price as well as put ... This is an updated version of my "Black-Scholes Model and Greeks for European Options" indicator, that i previously published. I decided to make this updated version open-source, so people can tweak and improve it. The Black-Scholes model is a mathematical model used for pricing options. From this model you can derive the theoretical fair value of an options contract. Of course, Binary Options pricing can be quite a complicated procedure. Indeed, most online resources will point people to explanations which involve advanced derivative mathematics like the black Scholes model. These are mainly used by OTC traders at global investment banks. This, however, should not deter you. If you can understand the main ... Black-Scholes option pricing model (also called Black-Scholes-Merton Model) values a European-style call or put option based on the current price of the underlying (asset), the option’s exercise price, the underlying’s volatility, the option’s time to expiration and the annual risk-free rate of return. The Black-Scholes Model n The version of the model presented by Black and Scholes was designed to value European options, which were dividend-protected. n The value of a call option in the Black-Scholes model can be written as a function of the following variables: S = Current value of the underlying asset K = Strike price of the option I'm trying understand something basic about Black-Scholes pricing of binary options. In my example above, the current price is over the strike price. The volatility is extreme but I'm still having trouble understanding why the price of the binary option (which I'm interpreting as the probability of expiring in the money) would be below 50 (50% odds). Assuming a random walk from the current ...
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