Last week, in embedding spot-vol correlation in option deltas, I showed how vol paths use anticipated changes in implied vol as the spot moves around to estimate more accurate deltas. It’s a maneuver that respects delta fully as a hedge ratio rather than its narrow textbook sensitivity of “change option price per change in underlying price, all else equal”. We are sure (enough) that all else ain’t gonna be equal, so we can use the knowledge to improve the hedge ratio.
The post explains how a “vol path” takes a slope parameter that dictates how ATM vol changes as spot moves. For example, a slope of -3.0 means a 1% rally drops ATM vol by 3% (ie from 20% to 19.4%, not 3 clicks such as 20% to 17%). It’s like a “vol beta”. We can even see -3.0 slope by looking at a 1-year beta between SPY and VXX based on daily samples.
A stylized view of how this works:
The vol path only affects the ATM vol. If the smile remains the same shape along the path, the vols of all the options also change. That’s not all. The skew, measured as normalized skew or the percent premium/discount of OTM strike vs the ATM strike, is also changing if the shape stays the same but ATM changes.
While vol paths describe the ATM vol, there are skew models that describe how all the options for a given expiry will change. Just like the vol path concept, the goal is to make better predictions of how a portfolio of options will react to stock movements without pretending that vols don’t change. This is an opportune moment to remind you that the presence of a smile in the first place is a patch to the faulty Black-Scholes assumption that vol is constant. If the strike vols don’t change as the spot moves, the ATM vol still does since you have “moved along the smile”.
The entire branch of quant devoted to modeling option surfaces stems from the knowledge that vols change as the underlying moves and that there is value in trying to forecast those changes rather than accept a null prediction of “vols won’t change”.
There’s no controversy about whether there is value in modeling the dynamics of option surfaces. Better models improve:
- Risk measures. VAR needs assumptions about how the surface reprices when spot moves. Your hedge ratios are direct outputs from portfolio scenario shocks and their assumptions.
- Market-making. Sound models mean the ability to recognize abnormal kinks within a name or cross-sectional divergences between names. A model gives you a baseline from which to judge “how strange is this surface change”? If the skew rips by X, do I expect that to pop back into line or is this within the realm of normal, given the market’s movements?
- Option pricing on illiquid names. How do I estimate option values in a name with sparse quotes? A good model fills in the blanks.
My goal with this post, like all of my posts, is not to give it an academic treatment but the non-quant practitioner’s perspective. To offer an intuitive angle to either better organize your understanding, whether this is new to you or if you come from a similar vantage point OR complement the textbook rigor that some readers possess.
As the title suggests, we are going to reduce the topic to 2 basic types of skew modeling approaches — “sticky strike” versus “floating”. The fact that there are 2 is a hint that neither is fully “correct”. Just like skew itself is a kluge, the entire domain of surface modeling is basically a kluge. Beyond hard arbitrage boundaries, the relationships of options to one another is a collection of informed guesses mediating a constantly evolving conversation between models and behavior.
The typical George Boxism “all models are wrong, some are useful” applies. Models are toys by necessity — if they were actual simulations of reality then the reality is simple enough to not need a model. Nothing about the future of a security price satisfies that requirement.
Our procedure here is to assert the model, see what they would predict if they were true, and then watch them break by hypothesizing the trading strategy that would profit from the models NOT breaking (which of course is a blueprint for why they must break).
The nice part is that this is mostly a visual exercise so don’t be discouraged by the post being too long to fit in the email…it’s a lot of pictures.
Floating Skew
A floating skew model says that the percent skew by delta* stays constant. The 25-delta put is always, say, 25% above ATM vol.
Note: Floating skew models are also referred to as “sticky delta” keeping consistent nomenclature with their counterpart “sticky strike”. I always found this similarity in names to be confusing but YMMV.
*Delta is a stand-in for any normalized measure of moneyness.
Log or percent moneyness itself (ie “a 5% OTM put”) is not normalized for volatility. A 5% OTM option on TSLA is a lot “closer” to ATM then 5% OTM on SPY because TSLA is so much more volatile.
Delta is a vol-aware unit of distance, but it has the problem of being recursive. We need a volatility to measure distance to measure the vol premium on a strike BUT we delta depends on the very volatility we are looking to parameterize.
You can use standard deviation based on ATM or .50 delta volatility to measure distance as I do here. I admit this might be cope as I’m just drinking the Heisenberg poison I’ve built immunity to. The stylized demos in this post are using the base smile from last week’s post from a SPY snapshot.
Spot = $695
ATM vol = 12.4%
DTE = 31We also maintain the -3.0 vol path (ie a 1% rally drops ATM vol ~3% and vice versa). This model says the percent premium/discount of a strike’s given delta is preserved.
Looks sensible if we plot vols by delta for green (stock up ~1% to $702) and red (stock down ~1% to $688):
Let’s plot vol by strike:
Hmm.
Let’s look closer. Again, the purple curve is the base curve. The green curve represents the smile if SPY jumps from $695 to $702, or ~1%, and the red curve represents the smile with an ATM strike of $688.
I’ll narrate observations, but it’s best to pre-load your own observations if you’re trying to learn (you’re enabling the technique of ‘hypercorrection’ or ‘surprise learning’).
Observations and notes on breaking
- The down move where vol increases due to vol path, actually leaves us with a lower ATM and downside vols! It’s because the vol path itself is not tangent to the slope of the actual skew of the purple line. In this model, unless the vol path is tangent, vol will underperform on the downside while the OTM calls will outperform. As the stock rallies, vols across the board outperform because the vol path is not as steep as the implied skew.
- If there were no vol path at all (ie vol slope = 0) then these under- and outperformances would be even more egregious. In fact, if that’s how surfaces behaved you would simply sell the slightly OTM puts and buy the OTM calls knowing that whenever the spot moved, the IV spread you had on would profit since the vol would always underperform on the way to your short and vice versa. It’s true that you’d still be exposed to changes in realized vol, but you’d have a giant IV tailwind as compensation.
- If the vol path was as steep as the skew, you’d be much closer to a sticky strike model to be discussed below, along with its own caveats, of course.
- A floating model is incoherent in the extremes. If ATM vol doubles/halves, all strike vols must double/half. Leading the witness a bit, but tails are sticky…which means skew flattens when vols get extremely high, and steepens when it gets its extremely cheap. The floor on a .10d put vol is proportionally higher than the realistic floor of an ATM IV. At the extremes, a single penny can be several vol points as prices get sticky (especially since transaction costs are fixed dollar amounts — think of the fee to sell an option at a “cabinet”.)
By asserting the same percent skew premiums/discounts across the curve, the strike vols themselves are left to vary as our chart shows. This view shows how the strike vols change from the base curve depending on whether the stock went up or down:
Sticky Strike
A sticky strike model asserts that vols do not change as the spot moves. The $680 put trades at the same vol whether SPY is $695 or $702.
If we fix the strike vol, what happens to skew?
If strike vols are fixed but spot rallies 1%, your 25-delta put is now a 20-delta put. Same vol. Different delta.
This chart is percent skew by call delta for the base curve. For the shape rotators in the audience, go ahead and guess what happens to the skew at the .75 delta when it becomes a higher delta call after a stock rally.
As a wordcel myself, I’m just going to display the answer.
Zooming in on the actual skew changes:
Put skew flattens (ie gets smaller) on sell-offs while call skew gets trashed. On rallies, put skew firms* and call skew flattens (becomes much less discounted).
*A 2% shift in normalized skew is “small”. If skew is 20% premium and ATM vol is 30%, that’s 6 points of premium. A 20% to 22% move in the degree of premium is 0.6 vol points. Matters to a market-maker but it’s noise to most participants.
Picture of SPY 1m .25d skew for the past year:
Zoomed in, you can see how it flattened during the late Feb to late March sell-off and bottoming ahead of Liberation Day before spiking!
I’m not making stories, but pointing out that it collapsed again on the second leg-down, marking the bottom for the remainder of the year. All hindsight stuff, but overall you can see the range for .25d put skew was about 15% for the year(from about 14 to 29% premium to ATM vol).
In case you need a reminder for why I don’t like trading skew for vol reasons:
a sense of proportion around skew
Reality
Sticky strike predicts flat strike vols.
Floating strike predicts unchanged skew, which describes how strike vols change.
Let’s pause for a second. I’ve done something subtle in how I’ve framed this discussion which might be lost on more novice readers (although I’m not sure just how novice anyone who has gotten this far might be).
Without saying so directly, I am putting a lot of emphasis on what happens to strike vols. For traders as opposed to onlookers who just talk about what vol or VIX is doing, strike vols are the closest thing to what matters — option premium. Strike vols influence option prices directly and prices of contracts determine p/l. “Vol went up today” means nothing if strike vols were unchanged and the stock is simply lower. Telling me that ATM vol is higher doesn’t tell me if a floating model just slid down the curve. “Vol” is an abstraction of strike vol is an abstraction of option premium.
With that out of the way, relating these models to reality starts with observation of strike vols. In fact, this is how such models are generated in the first place. Noticing, then fitting.
You could go crazy with examples, but I will do just a couple to give you enough fodder for your own consideration.
This was a SPY snapshot on 1/20/26 with shares down ~2%
Strike vols are up across the board.
Notice:
- Sticky strike wasn’t true. Strike vols moved.
- Floating skew didn’t hold either. If the strike vols were all up in an approximately even fashion in clicks (ie all vols up 1.5 points give or take .3 for near the money) then skew flattened (think of it this way…higher IV options were up a similar amount to lower IV options).
- You could describe the change as a parallel shift in sticky strike vols. A sticky strike type movement means the skew changes. In this case, the put skew flattened and the immediate call skew became less negative.
A 2% move in SPY is 2 standard deviations. I’m not surprised the surface didn’t adhere neatly to a model. Even vol paths are extremely local (a vol path of slope -3.0 would predict that a 2% sell off would lead to a 6% increase in vol and IV on the original ATM went up double that amount from 13% to 14.5%).
Let’s look at IBIT March expiry on Monday’s selloff. IBIT fell ~6%, about a 2 standard deviation move as well.
Here’s the change in strike vols.
In the belly of the curve, sticky strike was a great description of what happened. Strike vols barely budged, while the signature of the strike vol changes for options that are now OTM calls and puts looks like what a down move with a floating strike model would predict. Call vols up and puts vols down. Sticky strike in the belly, floating skew for OTM.
And while the SPY move looks like it rattled the market as the surface shifted higher, the BTC move had little effect on its surface despite both moves being ~ 2 standard deviations. The SPY move seemed unstable, while the BTC move was stable.
What do you do with this?
If all of this sounds confusing, it’s because it is! This is good news for vol traders. If it weren’t, the market would just be more efficient. In this example, BTC vols underperformed SPY for the same exact type of move. Inverting, that means there’s an opportunity for discernment, as you had 2 assets which had highly correlated underlying behavior but mismatched volatility behavior.
A question to consider given the vol moves…if you buy the now at-the-money BTC vols that haven’t budged or even the OTM puts which actually declined in vol to sell upside SPX or BTC calls, is this an opportunity? This is what vol traders think about for a living. You have desks that see the flow in everything and combine that info with the relative strength and weakness across parts of the surface (it’s the whole idea behind the vol scanner tool).
If you’re a market-maker, you don’t have the luxury of just scanning the markets to cherry-pick. You are deeply embedded in the price formation process since you must post a market. In illiquid names, you must do this with limited flow information. Having a vol surface model to generate fair values to quote around is not optional.
In commodity options, I toggled between sticky strike, floating models with vol paths, and hybrids (basically a floating model with a vol path and a skew correlation that allowed you to rotate or tilt the shape of the curve forward and backward).
Just like a vol slope parameter, these models affect your deltas.
I remember a particularly brutal period where vol was so heavily offered on up moves that when I eventually gave in and ran a much steeper negative vol slope, the change flipped my delta from being flat to short $20mm of oil. And of course, if you are long vol as it’s getting pummeled on the rally, that means your model is now saying you are short on the highs. After all, that’s the problem. The market is rallying, your calls are massively underperforming their delta and you are short futures against them!
But this sensitivity means you can’t be toggling your models all the time because how you model affects your risk. The goal is to model reality, but if you keep changing models like your name is DiCaprio, you’re going to put your risk in a blender.
This is a good place for judgment. You build an understanding of how the surface changes for various types of moves while acknowledging that this depends on the market context and open interest. If investors are well-hedged to the downside like they were in 2022 (the market sell-off and rise in interest rates were extremely well telegraphed), then you might expect put skew to underperform on the way down. You certainly don’t want to run a fixed strike model in that case.
You let the market’s surface changes act as a tell. If the market acts differently on a small sell-off and a big-selloff that’s expected. You don’t really gain information. There’s no null to reject. But if both types of sell-offs have muted reactions, that’s interesting. This is an orderly, expected, and perhaps even stabilizing event.
On the other hand, a stock up-vol up surface move is unexpected. That should inform the model you run. There’s an art to this. How long or how persistent should a behavior be before you can classify which model you should run? There’s no simple answer (again, thankfully!). Open interest and expectations are convolutions that direct whether something is a surprise or not. Surfaces react to surprise. Remember they already know that vol is not constant — it’s the delta in expectations about how volatile the volatility itself is that substantiates new surface behavior. Surfaces anticipate a band of random behavior without reacting because randomness is embedded in volatility.
Sometimes interest rates rise because of growth expectations. But stagflation will do that too. The vol surface will likely care about the difference. Oil might be rallying steadily because China is booming and the global economy looks rosy. It can also rally because there is no peace in the Middle East. The vol surfaces will distinguish between the 2 types of rallies. Your deltas will be vastly different for the same nominal options position depending on the backdrop.
I’ll leave you with this summary that captures what I generally, but loosely, expect when I see the stock market up or down and whether I think the move is stabilizing vs destabilizing:
