Option Spellbooks

When you learn a new language you ascend levels of competence. You start with everyday words and basic grammar with a goal of at least being comprehensible. This will unlock simple conversations, a milestone that enables and encourages regular practice. Like getting through the first month of guitar when you just wrestle with physical finger placement and learning your A, E, G, C, D open chords. The moment you can fluidly switch between the chords you can play the majority of music you hear on the radio. That’s when your learning takes off.

With enough practice in language or music you can think outside your native tongue or improvise in real-time. In skill acquisition terms, you have achieved “unconscious competence”.

Options are the language of risk

You start by mapping basic vocabulary to real-world sensation. “Long call” = “happy if stock go up”. With practice, you develop taste in how to use this vocabulary. In English, “I know how you feel” expresses empathy but you don’t say that to someone who just lost a loved one both because it’s not true (you don’t know how they feel) and because this comment awkwardly makes the moment about you. Well-intentioned commiseration clumsily executed.

Trade structuring can be clumsily executed too. You think something could double in the next 6 months and you…sold puts? If you are right, congratulations on making a tiny bit of cash on direction but opportunity costing yourself a small fortune by expressing the trade with a short vol position when your entire thesis insinuates orgasmic levels of vol!

You touched options without understanding that they are always about vol. Like knowing the words but not how to use them. You’re still stuck at “unconscious incompetence”.

Before you go further it will take 4 minutes to review this idea directly…see Translating to “option surface” language

Wizardry

You have a book of spells. You desire stealth so you look up “cloak of invisibility” and see you need some a salamander tail, a runestone and peroxide to conjure it. Common ingredients in a sorcerer’s home.

In investing you have a sense that a stock is “probably going higher but if I’m wrong I’m really wrong.” That’s a natural language description of a somewhat routine scenario. You need to translate that to code. Option code.

• What instrument is levered to the “probability that a stock goes up”?
  • A call spread (if this is not clear, review a deeper understanding of vertical spreads)
• What instrument is levered to “if down, magnitude is yuuuge”?
  • A far OTM put

So the package of “probably going up, but if down, then down big” can be represented in option language as “long a call spread plus a teeny put”.

That’s the name of the spell.

Now, as a wizard you can adjust the size, ratio, and particular strike to both

a) suit your taste and

b) take “what the option market is giving you”.

What the option market is giving you

This ties right back to the most underappreciated concept in trading….is it bid or offered?

If you believe that an asset’s upcoming moves are distributed so it probably goes up but if not it crashes, you know what spell to cast. That’s half the battle.

Next question:

Is the option market offering you the ingredients for the spell at an attractive price? Or is every wizard trying to cast the same spell and bidding for the same ingredients?

We are going to look at a couple spells and their cost of ingredients.

You’ll learn how to measure price, decompose recipes, and if you read between the lines you’ll notice — even when no trade is indicated you receive a valuable update to your assumptions or an opportunity to express the bet in a way that exploits the price anomaly. There’s a beautiful yin and yang to options. If the cost of a one spell gets expensive there’s a counterspell that gets cheaper with respect to your view!

Let’s get to some data.

Setup

We are going to look at 2 spells that can make sense for betting on “probably going up, but if down, then down big”. An interesting thing about this distribution how its kinda the base case distribution for SPY right? Both history and the options market agree that the SPY proposition looks like “hey you’ll make some money on average and every now and then there will be a big drawdown. also, don’t expect the market to crash up overnight”.

[💡That fact in itself is useful because if you think another market conforms to that distribution you know how the SPY option market prices that spell! You may even adopt a prior that the SPY price for that spell could be an upper-bound or be considered “expensive” if another asset started trading that way. If that’s hard to understand, don’t sweat it, it’s a slightly more advanced inference that a relative value trader might make.]

We are going to price the spells and look at charts.

• Our universe will be: SPY, TLT, GLD, USO and BITO
• Our date range is almost 4 years (Jan 2021 – Nov 15, 2024…except for BITO which start 10/21)
• We are looking at the closest listed expiry to the 90-day maturity (based on what option chains are listed there is about 15% tolerance on DTE around 90 but BITO chains are more sparse so DTE can vary by as much as 30 days or 33% tolerance)
• We are choosing strikes closest to breakpoints that are 1 or 2 standard devs OTM depending on the spell. If we measure strike distance with standard deviation we are using the ATM vol to define the SD. So if 2 assets are both $100 a 1 standard deviation OTM call will be further away (ie a higher strike) in the higher vol asset. This concept is detailed in these series of posts:
  • Breakpoints
  • Ratio’d

There will be lots of little observations along the way so in the spirit of “enough with the rulebook, let’s just play”, we’ll proceed.

Learning the method via SPY

The first spell we’ll examine is a package of:

1-s.d. / 2-s.d. call spread

+

2-s.d. OTM put

measured as a percentage of the spot price.

For example, on 1/12/2021 the details were:

The package cost 1.16% of the spot price on that day.

Exploring the long call spread + long far OTM spell

Let’s move on to charts. I will point out notable features of each chart. I’ll point out the bits of learning in each one.

Chart 1

🌙The red line is the price of the package. It ranges from about 70-150 bps for a 3-month expiry

🌙The blue line is the ATM call as a percentage of spot. If you remember the straddle approximation formula you know that by dividing the spot price out this measure will track implied volatility.

🌙The package is long volatility (you lay out premium for it) so it’s not surprising that its price is correlated with the vol level. You also see that the package price itself varies between something like 20% and 50% of the ATM call value. When vol is low, it’s a higher percentage of the call price. Ponder that for a moment. It means OTM options are a bit “stickier”. Skew as a percentage of ATM vol (aka ”normalized skew”) flattens as vol increases and steepens as vol softens. We’ve talked about before in the context of conditioning skew percentiles on vol levels by using scatterplots to see that skew has a curved relationship to vol.

Chart 2

🌙Same data in scatterplot form. You can see the correlation clearly (r = .76). Red dot is the recent observation (11/15/24). The package price is high compared to the vol level. I don’t like to anthropomorphize markets and say “the vol surface agrees with the statement that the market is likely to go up but if not crash” but the price of that expression or spell is high. The market is not offering it cheaply.

Chart 3

🌙Lots of smoothing — dark red line is the 200d moving avg of the package. The dark pink is the rolling 200d standard deviation of the package price. Dashed pink is the 200d MAD (mean absolute deviation — just another measure of deviation. If it’s close to .80 then the distribution of the stat is close to normal, if it’s less it’s fatter tailed. It costs nothing to add this metric so I tend to do it whenever I look at a standard dev just in case there’s a disparity from .80. The dashed light blue line shows that its stable at .80 even if it’s hard to see on that axis).

🌙The dark blue dashed line is the z-score of the observation vs a 200 day lookback. You can see the spike on 8/5/24

Chart 4

🌙I was just curious so I threw up a scatter of the package price vs the trailing 1-week return. It gets cheaper when the market rallies but that’s just the spot-vol effect. On large moves either way it does look like there’s some modest smile effect where even on a large up move the package is more likely be on the more expensive side. Maybe the most interesting part of the chart is the X-axis itself. You can see the left skew of weekly returns. There are more large up moves than down moves but 2 largest moves are negative and out of bounds compared to the rest of the blob.

Decomposing the spell: the price of the ingredients

Let’s look at the building blocks of the spell to see what’s driving the value of the package.

🌙In 2022, the bulk of the package price was driven by the far OTM put. But you can see some small stretches like October 2022 when equity markets bottomed for the year (lows that haven’t been touched since) where the call spread was actually more expensive than the puts! We’ll chart the ratio of the package to the ATM call price directly to see that the package got cheap relative to the vol — again the skew flattening (shaded region was Oct 2022 lows). In this case, it was the put skew especially that got hammered.

[I remember 2022 in vol markets as the year tail and defensive strategies massively underperformed because funds had boughts puts at the end of 2021, a frothy year in from which a sell-off was actually consensus. If a sell-off is stabilizing, and restores order to the force, the skew is not gonna perform.

Markets are biology not physics he shouts into the void. It’s poker all the way down. Notice how I don’t try to create rules from what has happened or play technical analysis. I just look for prices that are anomalous, which doesn’t mean wrong, it just means it deserves attention. From there you have to like think and stuff. Get used to sitting in paradox. There is no closure. Markets are utterly indifferent to your need for coherence.

For what it’s worth a similar setup happened in late 2018 — vols ripped into the Q4 sell-off but skew got crushed because of a large overhang of recycled downside vega from the autocallable structured products. There was an inflection point in the open interest though so a clever cat would realize you could load up on the hated, supplied region of the skew because the market’s outstanding vega profile would flip on a second leg down (ie well supplied to flat).

So what do you do there? One thing that you can do (and it worked) was buy the puts and hedge on a heavy delta in expectation of a rally. If it rallies, you win on the outsize delta plus the puts sliding up the skew curve as they become further OTM. If the market sells off into the abyss where the open interest and market-wide greeks quickly decay you are long vega into an exploding vol market. It was one of the easier risk-reward setups that comes along every now. I know I’m gonna get emails from retail traders asking about how you can plug into this and I’ll just preempt it now. You can’t. It’s an information game the propagates out from the OTC market and the all the risk reshuffling that gets farmed out in chunks to institutional vol desks. At some level it gets “into” the listed market but the scent has to be picked up higher in the chain of issuance to understand the arrows, dependencies, and inflections.]

Exploring the 1 sd collar spell

The next spell is the 1 sd collar (also known as a risk reversal or god help you if you trade commodities, “a fence”)

Long 1-s.d OTM.put

–

1-s.d. OTM call

Notice how this is put “minus” call. that means if the collar trades for a positive value then the put price > call price.

Again we will divide the package price by the spot price to normalize and we are still using 90 day maturity.

Let’s use USO, the oil etf. Instead of pointing out what’s interesting in each of the charts I will cherry-pick questions so you can practice.

USO:

Chart 1

🌙What does it mean that the collar price sometimes goes negative? Do you think you can spot the Ukraine invasion in the chart?

Chart 2

🌙 The collar price can get extreme in favor of the put OR the call at high volatility. Why might that make sense for oil?

Chart 3

🌙The chart starts in January 2021. The puts started the year high relative to the calls declined over the course of the year then flipped in 2022. What’s the story behind the change?

Chart 4

🌙Compared to the SPY chart’s x-axis earlier what do you notice about oil’s weekly returns?

The decomposition of the collar into the separate call and put legs will let you see the drivers.

In early 2022, you can see the put leg was relatively stable after peaking at the end of 2021 but the collapse in collar pricing was driven by the calls exploding higher.

🌙Can you see the Oct 7, 2023 Hamas attacks in the chart?

SPY collars

I’ll just point out the animal spirits in the stock market. SPY collars are relatively cheap these days.

The contribution of the legs to the cheapness looks balanced. Puts are a bit low and calls are a bit high.

BITO collars

BITO is an etf that tracks BTC futures. It’s performance is marred for the same reason VXX stinks. Negative roll returns as the prompt future must be rolled into a premium 2nd month in a contango (upward-sloping) futures market.

You can see the effect clearly in the BITO cumulative return chart but it’s still useful to see the point to point changes. Even though the cumulative return since its inception is -35% you can see that in the past 2 months its surged from -60% to -35% mirroring BTC giant rally.

Interestingly, it looks like when they were first listed, the calls were premium to the puts (negative collar prices) before establishing the familiar regime we see in many assets — the puts are premium.

[More story time: In the mid-aughts during the commodity “supercycle” there was a lot of noise about commodities as an asset class, financialization, yada yada. I was on the NYMEX floor when WTI first breached $100. IIRC a trader overpaid for a one-lot in the pit lot to own the memorialized print.

Anyway, call skew in the oil markets got annihilated with financialization. Why? Because to passive investors, calls are free money to be sold. So as something becomes financialized you have some prior about what will happen to the call skew. Something to consider for all those bulled up on IBIT calls these days. I’m not exactly sure what happened in BITO when it got listed, but maybe the first option quoter was still wearing footie pajamas back when commodities became an asset class.

As you can see from the USO charts, the skew in oil is fascinating because barrel prices can crash down like during COVID or up. From a long history of trading oil, owning the call skew has been positive expectancy because hedgers are a steady supply of upside-vol yet the true distribution includes crash-up potential.

This was also true in heating oil and gasoline. Gasoline is a smaller market than crude oil and less liquid. My approach to OTM calls in RBOB — buy em’ when they’re cheap, only sell them closing. Never open on the short side “because they screen high.” Same attitude in nat gas or anything that gets real sloppy on the upside as liquidity evaporates. There’s probably edge in being short because that’s where you’d expect the risk premia to live but the risk/reward and survival imperatives mean only those messing with other people’s money get wide-eyed at that stuff. I guess you could always trade it small but also maybe find other ways to deal with your boredom.]

Spellbooks

I’m not going to show charts for each asset but just summarize just show this self-explanatory spellbook.

You could imagine columns for decomposing the legs and their stats. On and on. You could see how one might want 10 screens.

[We don’t have this in moontower.ai but we’re excited about all the wood we’re gonna chop in 2025 😉]

Actually on the 10 screens bit — a normal human thinks that sounds like a nightmarish work environment. But you have to have some faith that this works just like walking and chewing gum. You get used to it. Plus all the dashboards are the survivors of the evolutionary screen-space tournament. What’s left is a bunch of tables and charts that your eyes easily scan and process into a gestalt. It’s like the market is having conversations all around you but a well-constructed cockpit will simulate the cocktail party effect — you’ll identify the most prominent features of what market parameters are changing today. This is the “science” part. The actions are the art.

Wrapping up

Some repetition and a smattering of observations that might not be obvious to learners

• Using 90 day options means we need to multiply the typical cost of these structures by 4 to annualize
• Assets vary in what a “typical” vol surface looks like. SPY always has a pronounced put skew. Coffee and VIX have inverted skews. Gold is usually a true smile with both far OTM puts and calls trading at premium vols to ATM. The same spell therefore varies in cost across markets.
• Decomposing spells will let you see what legs are driving the cheapness or expensiveness of the package.
• In keeping with the “options as a language” metaphor, volatility metrics like “implied vol” and “skew” can be seen as a abbreviations. Like if the put skew is high, the price of the collar will be high. But when you trade you don’t trade “skew” or “vol” directly but you trade contracts with actual prices. The vol metrics are handy ways to normalize in the same way that P/E is an attempt to normalize for comparison. But you trade actual instruments not metrics. As an option user, you open an option chain but its gibberish. Vol surfaces and metrics help you make sense of “all the numbers” on the screen with curves and historical context. We use the metrics to zero-in on what we want to do, but for execution we shift gears back into prices and strikes not vols and deltas. These spells are like a transformer layer between vol lens thinking and price thinking.
• You have an opinion about the market, but is your opinion bid or offered? The options market can tell you. Remember stock and asset prices in general are low resolution. Options are surgical. Just like parlays, the relative prices between the propositions imply tradeable ideas. Options are the coding language in which ideas are scripted into trades.