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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

As some commenters have pointed out in prior posts, I do

This is the first section also where you

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 lot of us have probably seen the term random walk, maybe in the context of

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

Most market participants have an idea of an asset'sIn 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).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 ofpossible 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)

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

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:

In the end, it doesn't matter either the

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

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

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)

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

Remember what I said about price formation being a gradual, continuous process? In the face of special circumstances, in particularly

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".

Price decoherence, mathematically, ends up being a more generalizable case of the phenomenon we all love to hate -

They have to unwind.

- Lily

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:

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:

# 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 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) =**24,000** **net 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:

**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:

**σ),** and has a few interesting properties:

# 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:

#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.

# Caveats/Read This

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:

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

submitted by the_lilypad to thecorporation [link] [comments]
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.

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.

---

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?

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:

Effectively, NOPE is a rough and dirty way to approximate the impact of

- 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.

**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**

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) =

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

(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.

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

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

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:

b)

2)

a)

b)

---

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

- 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.

- 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
- From the median, find the 30 days' median absolute deviation (https://en.wikipedia.org/wiki/Median_absolute_deviation)
- 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)

- 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!

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.

#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.

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

First -

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.

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.

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):

DTE | Strike | Premium | Intrinsic Value | Time Value |
---|---|---|---|---|

20 | $2.5 | $0.60 | $0.50 | $0.10 |

20 | $5.0 | $0.25 | $0 | $0.25 |

20 | $7.5 | $0.05 | $0 | $0.05 |

50 | $2.5 | $0.80 | $0.50 | $0.30 |

50 | $5.0 | $0.40 | $0 | $0.40 |

50 | $7.5 | $0.20 | $0 | $0.20 |

110 | $2.5 | $0.95 | $0.50 | $0.45 |

110 | $5.0 | $0.50 | $0 | $0.50 |

110 | $7.5 | $0.25 | $0 | $0.25 |

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.

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 | 10 days | 20 days | 30 days | 40 days | 50 days | 100 days | 120 days |
---|---|---|---|---|---|---|---|

A | $3 | $3 | $3 | $3 | $3 | $4 | $4 |

B | $4 | $4 | $5 | $6 | $7 | $12 | $14 |

C | $7 | $7 | $7 | $7 | $7 | $7 | $7 |

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!).

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!

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

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?

submitted by Xayde26 to wallstreetbets [link] [comments]
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

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:

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:

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!

submitted by hatitat to options [link] [comments]
There seems to be two general methods:

First Method: IV-Based

- One Standard Deviation Move = (P) (IV) (DTE/365)^0.5

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 [1] - 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**[2], 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**[3]. 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 [4] - 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 [5] - understood that this seems to be just an approximation. Should I be looking at formulas from 1988, however?

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) [6] OR
- Expected Move = (Price of Straddle close to Desired Time Period) / (Price of Underlying) [7]

In the end, I'm just trying to be as accurate as possible. Is there a

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!

submitted by rcrmlt to learnpython [link] [comments]
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.

submitted by ObviousTwist to thewallstreet [link] [comments]
Most of these link directly to pdfs (view, not instant-download).

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.

**Forecasting Volatility in Financial Markets: a Review**(60 pages)- Option Strategies: Good Deals and Margin Calls (40 pages)
- Option trading strategies based on semiparametric implied volatility surface prediction (30 pages)
- Short Term Variations and Long-term Dynamics in Commodity Prices (20 pages)
- Success and failure of technical trading strategies in the cocoa futures market (40 pages)
- The Information Content of the S&P 500 Index and VIX Options on the Dynamics of the S&P 500 Index (45 pages)
- The Performance of Model Based Option Trading Strategies (25 pages)
**evidence on the efficiency of index option markets**(15 pages)- OPTIONS EVALUATION - BLACK-SCHOLES MODEL VS. BINOMIAL OPTIONS PRICING MODEL (10 pages)
**ECB: risk, uncertainty, and monetary policy**(40 pages)- TIMING STRATEGY PERFORMANCE IN THE CRUDE OIL FUTURES MARKET (30 pages)
**An Anatomy of Futures Returns: Risk Premiums and Trading Strategies**(40 pages)- Roll strategy efficiency in commodity futures markets (40 pages)
**Spread trading strategies in the crude oil futures markets**(35 pages)**Commodity Strategies Based on Momentum, Term Structure and Idiosyncratic Volatility**(20 pages)- AN EXAMINATION OF MOMENTUM STRATEGIES IN COMMODITY FUTURES MARKETS (30 pages)
**understanding crude oil prices**(45 pages)**BONUS BOOK: The Bond and Money Markets: Strategy, Trading, Analysis**(1150 pages): a comprehensive textbook on bonds, interest-rate derivatives, money markets, credit derivatives, yield curve analysis, structured products, CDOs

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:

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???

submitted by midgetginger to options [link] [comments]
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

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 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 ... 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 ... Black Scholes formula assumes that the volatility is independent of strike price and maturity. This means that the implied volatility should be a flat plane. Prior to 1987 stock market crash this was indeed the case. Surprisingly now the market has changed and implied volatility of an options contract now depends on strike price and time to expiry. Due to this reason Black Scholes formula ... *Remember the Option price presented, and the Greeks presented, are theoretical in nature, and not based upon actual option prices. Also, remember the Black-Scholes model is just a model based upon various parameters, it is not an actual representation of reality, only a theoretical one. *Note 1. If you choose binary, only data for Long Binary ... 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. Black-Scholes Binary System is an high/Low strategy. This is a based on the complex metatrader indicators. Time frame 5 min, 15 min, 30 min, 60 min, 240 min, daily. Markets: Forex, Indicies, Commodities. Expiry time 5-7 candles. Black Sholes Binary is also good for trading withaut Binary Options. b. don't really know about market price of risk. c. In this case the pde is the same as the black scholes pde using your risk neutral process. Can you think of why this is? Does the type of call option change how the underlying changes? What are the other boundary conditions ie (for S = 0 and S = infinity). Take a look at dirichlet (also known ... effort binary option price black scholes to create a quick screenshot of your person living. What makes forex trading signal systems provide a free Walmart gift not be able to meet all your data includes a warranty; If you follow these vary from time there happens to be called the turning towards currency notes are Essential – Scholes Formula and Binary Option Price Chi Gao 12/15/2013 Abstract: I. Black-Scholes Equation is derived using two methods: (1) risk-neutral measure; (2) - hedge. II. The Black-Scholes Formula (the price of European call option is calculated) is calculated using two methods: (1) risk-neutral pricing formula (expected discounted payoff) (2) directly solving the Black-Scholes equation with ... Price of a digital call option under Black Scholes: Given previously: r = 0.05, t ... solution for the binary option in the Black-Scholes method and numerical solutions for the Explicit Finite Difference method, the Forward Euler- Maruyama method, and the Milstein method. Examples were provided in all cases for the numerical methods to conclude that all three numerical methods provide valid ...

[index] [24378] [14197] [12235] [16809] [12840] [17963] [19062] [10480] [29449] [1397]

Exotic options: binary (aka, digital) option (FRM T3-44) ... Black-Scholes Option Pricing Model -- Intro and Call Example - Duration: 13:39. Kevin Bracker 288,547 views. 13:39. Language: English ... 2/2016 Thammasat University, 5702640250 Jun Meckhayai 5702640540 Nattakit Chokwattananuwat 5702640722 Pakhuwn Angkahiran 5702640870 Pearadet Mukyangkoon 5702... Some time back, my student asked for my help to build a calculator to calculate call and put option prices and the option greeks. So, I thought I will just d... Further, the Black–Scholes equation, a partial differential equation that governs the price of the option, enables pricing using numerical methods when an explicit formula is not possible. A walkthrough of the Black Scholes Option Pricing Model on a Spreadsheet. Spreadsheet file is linked and available in Google Docs. Link for video is tinyurl.... Introduces the Black-Scholes Option Pricing Model and walks through an example of using the BS OPM to find the value of a call. Supplemental files (Standard ... Black-Scholes Option Pricing Model -- Intro and Call Example - Duration: 13:39. Kevin Bracker 287,224 views. 13:39. How The Housing Crash Will Happen - Duration: 20:49. ... Black-Scholes Option Pricing Model -- Intro and Call Example - Duration: 13:39. Kevin Bracker 285,613 views. 13:39. Gold will be explosive, unlike anything we’ve seen says Canada’s billionaire ... 📱 FREE Algorithms Visualization App - http://bit.ly/algorhyme-app Quantitative Finance Bootcamp: http://bit.ly/quantitative-finance-python Find more: www.glo... Welcome back to statistics class. Undoubtedly more important that understanding the Black-Scholes model for pricing (which we purposely don't cover) is your ...

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