At the close of Friday, I was looking at far OTM gold put spreads.

With GLD at $275, the April 251/249 put spread is similar to a binary bet that GLD expires below $250 at expiry or about a 10% sell-off.*

You get 39-1 odds.

This is using market-based pricing, net of skew.

At-the-money vol is 16%.

Turns out 39-1 is about the right odds if we use 16% as a standard deviation. When I say “about right” I simply mean the gold left tail is basically conforming to an out-of-the-box Black Scholes distribution. I don’t mean B-S is “right” just that the put spread odds conform to what the B-S would say.

I wouldn’t expect that for SPX puts, but gold downside doesn’t have that much skew or tail fatness.

See the table mapping ATM vol relationship to the likelihood of ~10% selloff in a Black-Scholes world:

But a lesson that is far more important jumps out:

Implied volatility—the second moment of the return distribution—has almost no direct connection to the probability of catastrophic price moves!

Look how likely a 1-month 10% selloff is as a function of implied vol. If vol is 15% instead of 12% such a sell-off is 4x as likely and if it’s 18% instead of 12% it’s 10x as likely.

Just think of VIX…it can easily be 12 or 18, right? But what you should really take away from that is that volatility tells us very little about the tails.

Option Pricing on the Wing

A few things option traders learn early about pricing tails:

1. At-the-money volatility tells you nothing about the true probability of large moves.

2. Tail risks are not just “scaled-up” versions of small market moves.

3. Historical data is almost useless for extreme events because of sample size is too small to build robust probability estimates.

Instead, traders price tails based on…other tails.

Not backtests.

I invite you to keep your eyes open for sales pitches that pretend they know the likelihood of extreme moves and how they claim to know it. And if the sample sizes weren’t small enough, marketers might try to condition the probabilities — “when the market does X the probability of an extreme event does Y” which reduces the sample sizes even more. Godspeed with analysis that looks like that.

Inferring tail behavior from the meat of a distribution is so sensitive to small changes in volatility — so sensitive that it’s a clue that they’re not strongly related. I’m not making a math argument (I’m sure many readers could say what I’m saying formally). It’s a common sense observation that falls out of the volatility itself being volatile and sensitive to sampling.

The true odds of extreme moves are unknowable but there’s no reason to think they move increase an order of magnitude when VIX goes from 12 to 18, or for that matter, get cut by an order of magnitude when VIX falls from 18 to 12.

*The concept explained in a deeper understanding of vertical spreads

This post is an excerpt from the finance part of why home prices could fall with mortgage rates. 

I extracted it because it is a tidy explainer of something you feel but might not be able to articulate.

The reason you feel that selling your home to buy another these days feels like you have somehow incinerated money, is because you are.

It’s just bond math — you are buying a loan that is trading at a massive discount back for par when you pay off your mortgage. We can compute just how much money you are incinerating.

Quite unfortunate because along with low-supply and bottlenecks this is financial force that also conspires to remove supply and liquidity.

Excerpt below…

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Houses are worth very different amounts to existing homeowners vs buyers. And since many buyers are homeowners (I’m talking about people changing primary residence not second homes), the split valuation even exists within the same brain. You’re Hyde when you list and Jekyll when you bid.

Let’s walk through it.

Homeowners who secured low-interest-rate mortgages years ago effectively “shorted bonds”. As interest rates rose, the value of these loans plummeted, embedding equity into these “short bond” positions. This means that the mortgage itself has become an asset that is highly valuable to the current owner. It’s like “it’s equity in a mark-to-theo short”. But that equity is trapped. It’s specifically tied to that home. The new buyer doesn’t get it because they must finance at the higher current rates.

This mechanically alters fair value of the asset depending on who owns or doesn’t own it. The homeowner might not be able to articulate it but they have two assets: the physical home and the valuable low-interest-rate mortgage. If they were to sell the home, they would have to buy back the mortgage at its face value, rather than its current impaired value thus losing the accrued profit from the “short bond” position.

Let’s make it concrete with a numerical example.

You bought a $500k house 5 years ago with a $100k down payment. You borrowed $400k at 3%.

What do you owe today?

Step 1: Calculate the Monthly Payment on the Original Mortgage

The formula for the monthly payment of a fixed-rate mortgage:

Where:

• M = monthly payment
• P = principal loan amount = $400,000
• r = monthly interest rate = 3%/12 = 0.0025
• n= number of payments = 360

Monthly payment = $1,686.42

The mortgage still has 25 years (or 300 payments) until maturity.

The remaining balance after 5 years is $355,625 (from this calculator)

In our fake world that’s pretty similar to the real one, a lot has changed in 5 years. Interest rates have doubled to 6%.

What is the value of the outstanding mortgage?

Step 2: Calculate the Present Value of the Remaining Payments

We need to find the present value of these remaining payments, discounted at the current 6% market rate.

The formula for the present value of an annuity is:

• M = $1,686.42 (monthly payment)
• r = 6%/12 = 0.005 (new monthly interest rate)
• n = 300 (remaining payments)

PV = $261,744

The present value of the remaining ~$356,000 mortgage, when discounted at the current 6% market rate, is approximately $261,744.

This significant difference highlights the additional equity embedded in the homeowner’s “short bond” position due to the lower interest rate. The homeowner has an intuitive sense that they are losing when they sell the home because they will have to pay the bank $356k to close the loan when it’s only worth $262k. Eww.

The additional $94k of equity that the homeowner has at prevailing interest rates represents almost 20% of the value of the $500k home!

If mortgage rates fall, the conventional wisdom that marginal demand to buy should increase is a fair assumption. However, rates falling cuts directly into this shadow equity that owners feel compared to a high-rate environment. I suspect this will actually “loosen” a bunch of trapped supply as the bid/ask spread narrows as the homeowners embedded equity in their “bond short” shrinks.

[I’m using the word “shadow” but it’s quite real vs the alternative of buying the same house for $500k at the higher interest rate. It’s “shadow” because the only way to monetize it is to let time elapse until the mortgage eventually goes away. Your lower cost of living relative to someone who doesn’t have a low interest-rate mortgage on the same property is the only way to realize the equity.

Active solutions to this illiquidity trap is allow homeowners to somehow port their mortgage to a new property or allow them to buy back their mortgage at the current value instead of the remaining principal amount.

I already hinted at a passive solution. Let the clock run. As time progresses, homeowners continue to pay down their mortgages. With each payment, the principal balance of the mortgage decreases, and the equity in the home increases. Over time, the impact of the low-interest-rate mortgage diminishes as the remaining balance shrinks. This gradual reduction in the outstanding mortgage balance reduces the value of the “short bond” position, making it less of a factor in the homeowner’s decision to sell. Eventually, as the mortgage balance becomes smaller relative to the home’s value, the embedded equity becomes less significant, narrowing the bid-ask spread.]

If mortgage rates fall in concert with the economy and employment weakening (pretty standard backdrop to falling interest rates), then supply may loosen in combination with general demand shortfall. It feels like a downside risk…but by now I’m also resigned to believing home prices won’t fall. We don’t have enough of them. Lending standards are conservative. There’s nothing frothy about the supply/demand balance. At the same time, it’s illiquid and unaffordable. My selfish position is I’d like to see prices ease but I’d happily settle for a wider selection of homes, even if they are overpriced.

Last week, we launched the Portfolio Visualizer in moontower.ai

It’s a tool for using vertical spreads to make directional bets.

Input: You enter a target price and expiration

Output: It shows you a matrix of every out-of-the-money strike combination up to the target in terms of what odds it pays.

A quick refresher on the utility of vertical spreads

I’ve written a lot about them but as a refresher, vertical spreads are clean ways to bet on a terminal price by a certain date.

• You know your max downside so you can put them on without worrying about being shaken out of them by marks. I call this “risk budgeting” a trade
• Spreads, especially tight ones, have largely offsetting greeks. When you use an outright option to bet on direction you are expressing a view on a basket of parameters in addition to direction — most notably volatility and its doppelganger time. You can be right on direction and wrong on the other parameters. Using options demands a view on volatility (ie the “volatility lens” I’m always droning about). Vertical spreads discard this requirement because the vol and time exposures are heavily neutralized.

The fussy reader will raise their hand, as they should.

“What about skew?

Doesn’t the implied skew impact the vol differential between the 2 strikes of a vertical spread?

How do I know if the odds are a good deal?”

These are awesome questions. Let’s get to work.

The goal: develop a sense of proportion about how much “high” or “low” skew impacts the odds

Payoff Visualizer

Let’s start with some odds.

We’ll look at the payoff odds for call spreads on SLV and USO etfs on trade date 2/25/2025.

We are looking at approximately .50d – .25d call spreads for expiry 4/17/2025.

In other words, buying roughly an ATM call vs selling a .25 delta call expiring in nearly 2 months.

SLV

Lower strike: $29.50

Lower strike implied vol: 24.9%

Higher strike: $32

Higher strike implied vol: 27%

Measured skew = .27 / .249 – 1 = +8.4% premium

The call spread is marked at $.57 vs a maximum value of $2.50 offering 3.4-1 odds if SLV expires above $32.

💡Note that if the 32 strike’s implied vol increased, all else equal, the spread would decline in value, the skew premium would be higher, and the buyer of the spread would get even better odds. It seems counter intuitive but by increasing the skew and pumping up the 32 strike call, the market is saying 2 things at once:

• the magnitude of the upside of the distribution is fatter (the call is expanding in value)
• the probability or hit rate of SLV going higher is lower — you are getting better odds to be long this binary outcome

This seemingly offsetting sentiment makes sense. If the upside magnitude is higher AND the hit rate is higher then the stock price must also be higher. But if we hold the stock price constant and just move the implied skew, then we are adding clay to the middle & downside of the distribution AND the further upside BUT removing it from the nearer upside.

In sum, silver has positive call skew and the .50d-.25d call spread with 2 months to expiry offers 3.4-1 odds.

Now let’s look at oil.

USO

Lower strike: $76

Lower strike implied vol: 27.9%

Higher strike: $81

Higher strike implied vol: 26.9%

Measured skew = .26.9 / .279 – 1 = -3.6% discount

The call spread is marked at $1.59 vs a maximum value of $5.00 offering 2.1-1 odds if USO expires above $81.

🔬What you should notice

USO vols are similar to SLV but the call spread .50d-.25 delta call spread is much more expensive (and pays less than 2/3 the odds of the SLV call spread). Skew is driving the disparity. In USO’s case, you are selling the topside call at discounted IV to ATM, but in SLV you selling a premium IV.

Weighing in on whether this is a structural mispricing of the probabilities is not where this post is going. That’s more of a research question. Knock yourself out, if you want to dig up the empirical distribution of returns. I can point to reasons why the skews look like this.

1) Spot-vol correlation

SLV vols tend to increase as silver rallies. Part of the precious metals as risk-off, fiat hedge rubric. Oil is a risk-on asset usually with demand for energy correlated with global demand growth. Like stocks, it has a negative spot/vol correlation. However in times of middle east geopolitical stress the spot/vol correlation can flip to positive.

2) Hedging

Producer hedging in oil markets tends usually involves buying puts or put spreads and selling calls. While consumers (ie airlines and refineries) are natural buyers of oil, their hedging requirements are typically swamped by producers.

[The vol inclined reader will notice that these reasons explain the skew but don’t rule out the call spreads being mispriced. The implied skew reflects the supply/demand for vol at various moneyness, but that’s not the same as saying the implied skew predicts the distribution. If you want to bet simply on directionality in a given time frame, taking advantage of the skew is a perfect use case for the risk-budgeted vertical spread. If you are not dynamically hedging, you are not concerned about the conditional behavior of vol as spot moves around.]

The key lesson of the discussion so far:

The level of skew, the percent premium/discount, is a major driver of the vertical spread price and therefore the payoff odds and implied probability.

An inferred lesson, that is not really surprising, is that different assets have different skews. Nobody is ever going to price a SPY surface with silver skews. Both the distributions and spot/vol correlations have different properties.

To develop a sense of proportion around how the range of measured skew affects payoff odds requires looking at assets idiosyncratic skew behavior. In moontower.ai, we display both time series for skew parameters as well as percentiles

Between knowing if the skew is “high” or “low” compared to history and seeing the payoffs in the visualizer we come to a practical questions that tie it altogether:

If .25d puts are in the 10th percentile vs the 90th percentile, how much is that going to change the odds offered on my put spread hedge?

If skew is at “average” levels what kind of odds should I expect on a 2-month .50-.25d call or put spread?

The remainder of the post will dive into these questions so you can walk away not only with a sense of proportion but be able to form your own rules of thumb so you can quickly handicap values like how much extra your paying for a put spread when skew is “low” or how much more your getting for selling a call spread when the OTM calls are cheap?

Here’s a few thoughts for everyone before we get to the paywall:

1) Tradeoffs

For a directional bet, I don’t really see which spread to buy as a question of “what’s optimal?” You’d need an very fine-grained view of the distribution to identify that. Instead, I see a menu of tradeoffs between hit rate and payoff which the matrix displays naturally. In fact, just looking at the screenshots above of the matrix is very educational.

The matrix is the view I’d construct ad-hoc when I want to take a shot. I didn’t map the whole thing but I’d I basically run the same payoff calculation in my head by eyeballing a bunch of strikes, perhaps according to which option markets were tightest or have meaningful OI for liquidity purposes. It makes life easier to just have it organized in a matrix this way.

2) The hips and the fist

In any fighting sport you learn that power comes from the hips. The fist is just conduit that channels the power. When thinking about a directional bet, the work really is upstream of the options. The options are just the fist. It’s the easiest part. Most of the alpha power comes from the directional analysis. Or sticking your finger in the air.

Developing a sense of proportion about skew

We need to do 2 things to answer the practical question of how much does “low” or “high” skew in name change the value of the vertical spreads in real-life:

1. We need to see how much skew varies in a name
2. We need to run extreme skew parameters thru an option pricer to see how the spread’s price range (and therefore payoff odds) varies with the skew parameter’s range

Skew Variation

I did a small study of 3 names with different skew properties. I looked at 3 years of data to find the .50d IV as well as the .25d put and call skew parameters for options with about 2 months until expiry.

🗒️Notes on method

a) I allowed a tolerance of 50-70 days until expiry (that means there wasn’t necessarily a qualifying expiry for each trade date but there’s enough data points to get the gist).

b) Skew parameter = .25d IV / .50d IV – 1 … you can interpret that as a percent premium or discount to the .50d IV.

If .50d IV is 30% and the .25d put is 33%, then skew = +10%

💡Sometimes you’ll hear the term “clicks” or “vol points”. In this example, a 10% premium corresponds to 3 vol points or clicks.

Let’s just jump to the data which I think is mostly self explanatory now that you know the definitions. For each name I show the scatterplot of skew vs .50d vol level for:

a) .25d put

b) .25d call

c) .25d put – .25d call risk reversal

Remember unless it says “clicks” the skew parameter is in percent of .50d IV

USO

QQQ

SLV

Substack’s not the greatest for delivering these charts but you can always right click on the image and “open in new tab”.

The charts are nice because you can see that skew can vary with vol level. That’s discussed in the “key observation” stickies. Those stickies also show how skew is not some abstract idea — its specific behavior matches the specific properties of the underlying asset. Sometimes oil panics up or down. The tech index doesn’t panic up (even if single stocks in the index might).

We can get lost in reflecting when our goal was to see how much the skew varies in a name. This table will make it clear:

We can ignore the risk reversal. I included it because it took no extra effort. Instead, let’s focus on .25 skew. Again, just eyeballing, we can see that the interquartile ranges for put and call skews are typically around 5% wide (silver is a bit wider). Meaning that from the median to the 75th or 25th percentile you are only talking about changing the OTM option’s IV by about 2 or 3% of the .50d vol.

So if median put skew in QQQ is 16.2% premium to .50d IV and skew blows out to the 75th percentile than it goes to 19% premium.

If QQQ ATM vol is 20% your talking about a put IV going from 23.2% to 23.8%

How if QQQ IV is in the 25th percentile?

If ATM vol is 20% then the put is 13.3% premium or 22.7%

If skew went from the 25th percentile to the 75th, the put vol increases from 22.7% vol or 23.8% or just over 1 click.

Is one click a lot?

That’s the question we’re after.

Put spread sensitivity

We can test this using a Black-Scholes calculator.

We can compute a 60 day .50d put at 20% IV vs a .25d put at 22.7% IV.

This represents “cheap” put skew in the 25th percentile.

We will do this on a hypothetical $100 stock.

The .50d put will be actually be in-the-money slightly as opposed to at-the-money.

[See Lessons from the .50 Delta option for an explanation]

We end up with the 100.50 strike vs the 94.50 strike. This $6 wide put spread represent the .25d wide put spread.

When the skew is “cheap”, the IV differential between the strikes is 2.7 vol points (ie 22.7% – 20%).

The put spread is worth $2.03

[The 100.50 put is worth $3.50 and the 94.5 put is worth $1.48]

If we raise the skew to the 75th percentile, the 94.5 put goes to 23.8% IV and a price of $1.62

The put spread drops in value to $1.89

Again, notice when the put skew expands, the put spread drops in value! The left tail is getting fatter but the intermediate down move is losing distributional mass.

This is the put spread as a function of the vol differential between the 2 strikes. As the differential widens (the smaller put increasing relative to the .50d put) the spread gets cheaper.

What happens in odds space?

If the put spread is $2.03 and can be worth as much as $6.00 a buyer is getting 1.96-1 odds.

When the put spread gets cheaper, the buyer gets better odds of 2.17-1

In probability space, you go from 33.8% to 31.5% probability of expiring lower by expiry.*

The put spread changed in value by about $.15 on a $2 put spread as skew went from the 25th to 75th percentile all else equal. Given the variation of skew in QQQ it’s like every 3 cents in the put spread is 10 percentile points.

I won’t step thru it as slowly as I did with QQQ but here’s oil put spreads varying from 5% to 10% to 15% skew for the 100-91.5 put spread (.25d wide put spread):

Context is everything

When I was trading oil, a giant move in skew would mean, on a delta-neutral basis, a $5 wide spread would move 3 cents. If you made a nickel wide market on a put spread you’d be accused of making a market the broker could “drive a truck through”. In percentile space, you can see why.

But then again, you could argue that the exchange fees and broker commission represented a few percentile points.

If you are an options market maker, translating what low or high means to actual prices is important. It gives your market width context with respect to the surface parameters that you track. It lets you estimate how much edge you need to pad your market compared to how wrong you can be about how the surface might reprice.

On the other hand, if you are a purely directional trader the the difference in skew being low or high might be immaterial to your decision to take the odds unless your are able to discern probabilities down to just a few percent.

Now when you see a skew time series for a fixed maturity you know you can put the parameters in an option model and see just how much it changes the spread value.

You can derive your own sense of proportion customized to the context you trade in.

I’ll wrap by emphasizing that I’m writing from the perspective of mapping skew parameters to actual spread pricing. Trading skew on a delta-neutral basis because you think realized or implied vol will out or underperform as spot price travels across various strikes is a different animal. That is less about distributional outcomes and more about dynamic vol behavior. You care about what IV does when your vegas expand and contract, and what realized does as spot moves through your dollar gamma profile. It’s highly path-dependent. The opposite of a terminal risk-budgeted bet. In fact, the 2 different approaches can prescribe opposite trades meaning the risk-budgeted trader and the dynamic hedger can happily trade with each other. A classic example is the 1×2 ratio spread. The directional trader might use jacked put skew to buy a 1×2 put spread creating a highly attractive payoff profile in most scenario, while a dynamic hedger might be happy to own the 2 options because they expect vol to scream higher as the stock goes down.

For fun: What the most you’d be willing to pay for a $15/$10 1×2 put spread? The least? If you paid zero for it, can you lose?

Update 8/2025:

I was asked if I had written anything on the impact of events on skew percentile measures in the Discord. Sharing widely:

I haven’t, but most events are just one-day pricing problems. The effect of skew from 1-day pricing is heavily diluted if you are looking at 1-month skew and beyond. If you are looking at percent skew in like 1 week options, well all kinds of measurement issues anyway:

1. IV on 1-week options alone is a hairy topic since assumptions about how much vol time remains become impactful. Which is why if I’m trading near-dated, I really just think in terms of straddles and the price of vertical spreads. For the latter if a stock is trading 102.50 with 3 days to expiry you simply ballpark that the 100/105 call spread should be about $2.50 which is about the same saying the 105 call and the 105 put are equal (HW: prove this with put-parity). All the weird lognormal Black-Scholes math really melts away in the short term and you are in the realm of common sense handicapper.

2. The vega of options gets small in near-dated options so…maintaining a sense of proportion if important. If the ATM vol is 20% and the skew is 10% (ie 22 vol) vs 15% (23 vol) and the vega is 0.005 you haven’t even changed the value of the vertical spread by a cent even though the skew is 50% larger. I have written about this “sense of proportion” stuff. People get caught up in metrics that when you translate back into price space matter on the order of “it’s like paying an extra commission charge to IB on the trade”. In other words, if the difference changed your decision to trade, then the rest of your infra better be medical grade accuracy bc you’re trading for slivers.

On Jan 28th, one of my favorite topics came up in the Moontower Discord: natural gas options!

I was asked why the VRP was so low.

Recall VRP is the comparison of implied vol (forward looking) to realized vol (backwards) looking. In this datapoint,

One month IV = 49%

One month RV = 86%

The strange datapoint is a perfect icebreaker for discussing:

• seasonality (which happens to be most strongly expressed in natural gas)
• a common pitfall (and potential correction) for VRPs

   

Background

Before discussing options, we need to understand the shape of seasonality and the fundamentals that drive it. I’ve said many times that I’m not a fundamental trader. That means I don’t position based on any views about fundamentals. But a basic understanding of fundamentals is necessary to make sense of why an asset’s vol surface looks the way it does.

Let’s begin…

 

A Brief Primer on Natural Gas Dynamics

Natural gas prices follow a seasonal cycle, with volatility peaking in winter due to heating demand and spiking again in summer due to electricity consumption.

Seasonality volatility

Winter is the most volatile season.

• Heating demand: Cold weather drives demand
• Supply constraints: Limited storage or pipeline capacity can trigger price shocks.
• Weather uncertainty: Forecast swings can cause sharp market reactions.

Summer is the next most volatile season.

• Electricity demand: Power plants burn more gas for cooling
• Hurricane season effect on supply: Storms in the Gulf can disrupt production

The Storage Cycle

• Injection Season (April–October): Gas is stored for winter, with October marking peak supply. If storage maxes out, prices can collapse.

  [In 2009, this was a major risk with the Oct $2.00 put price surging to an insane vols on extremely heavy volume. I remember feeling terrible for leaving my business partner to deal with that expiration on his own because I had to be in Mexico for my wedding week. He was able to join the festivities after making sure we weren’t going to need a cave to take delivery. I distinctly remember computing that the stretched IVs still never reached the extreme levels of realized vol that accompanied that expiry. On a hedged basis, every option except the ones where Oct gas expired were a buy. The market found the path of maximum pain.]

  Injection season is often traded as a package of futures of options known as the “J-V strip” based on their futures month codes. In trader language, the “ape-oct strip”.

• Withdrawal Season (November–March): Stored gas is used to meet demand, with March marking peak depletion—low storage levels can drive price spikes.

  This season is also traded as a package — the “X-H strip” or “Nov-March”

…which brings us to the “widowmaker”.

 

March-April Spread: A Market Tightness Gauge

The March-April futures spread more affectionally known as the “widowmaker” or simply “H/J”:

• High March premium: Indicates low supply and potential scarcity.
• Weak or negative spread: Suggests ample gas and lower risk.

I’ve written at length about this spread and the options on it.

🔗What The Widowmaker Can Teach Us About Trade Prospecting And Fool’s Gold

You can learn a lot from its vol surface that can be applied to any asset with a “bubble” distribution. Moontower’s ever-so scientific definition: a price that most likely collapses but can reach any arbitrarily high price before it tanks.

🔗What Equity Option Traders Can Learn From Commodity Options

 

Supporting evidence in pictures

 

Exhibit A: Natural Gas Inventory 5-Year Seasonality Chart

Exhibit B: A historical snapshot of the gas futures term structure

Exhibit C: Realized vol by month

Exhibit D: Despite the strong realized vol seasonality the range of volatilities both across and within years is itself quite volatile.

Exhibit E: The March/April futures spread

The “widowmaker” expires this month. In commodity land, futures spread are usually quoted as near month – back month. So in a backwardated market the spread would be positive (ie March > April).

In equity markets the convention is reversed. The price is quoted as back month – front month. The charts below are from IB which uses equity market convention.

You can see the “winter premium” come out of the spread as April is now trading close to parity with March but the spread was negative (ie April < March for the past several months).

This is typical behavior. The spread usually goes to parity as the fear of a cold winter subsides. But it’s dangerous to short early in the season because the spread can go extremely negative (if you’re looking at the price using the IB quoting convention…which burns my eyes but whatever).

Here you can see the spread for 2026. April is trading at about a 32 cent discount to /March (~10%). If next winter is mild, you’d expect the gap to close.

In the below charts we respect tradition by using the quoting convention of March – April…you can see the destination of the spread is usually ~ 0:

This was the spread in 2007 when John Arnold became a legend stuffing Amaranth’s Brian Hunter’s attempt to squeeze H/J:

 

Option surface dynamics

Let’s see how these fundamentals influence the vol surface.

Skew Feature

🔀Inverted skew

Call IVs typically trade at premiums, often steep premiums to puts. Because gas is prone to squeezes it often maintains a “spot up, vol up” dynamic. On the downside, gas can find incremental demand via “coal-switching” whereby gas prices become competitive with coal as a input to electricity generation. This source of demand dampens vol as futures fall reducing the probability of a complete collapse in an oversupplied market.

This is a chart of Feb gas options (note that Feb options expire in January…in commodities the contracts are named after their delivery month not their expiry month). The curves represent roughly 2 weeks and 3 months to expiry. You can see the skew inversion.

💡Learning moment: Note how skew looks steepens when DTE is smaller. Much of this is an artifact of the X-axis being in strike space not delta delta space. Why does that matter? Because how “far” a strike is depends on time. If gas is $3.00, then the $3.20 strike is much further (ie lower delta) with 2 weeks to go than 3 months to go. Low delta options usually command premium IVs.

 

Term Structure Feature

📅Seasonality in the forward vols

We know that realized vols are higher in the Winter. Look at the vol term structure I pulled from the futures options via CME.

2 things to note:

1. LNF6 and LNG6 slope upwards indicating a higher volatility than Q42025 vols. This makes sense those 2026 capture December and January coldness while LNZ5 December options only capture through Thanksgiving. This tracks, nothing weird.
2. Those winter vols implied vols are LOWER than Spring 2025 vols (ie LNK5 or May). What the heck?!

You have 2 forces colliding from opposite directions.

a. We absolutely expect vol to be higher next winter than this spring

b. Deferred futures contracts don’t move as much as prompt ones.

In other words, the beta of those winter contracts to whats happening now is low. Today’s supply/demand balance for gas has only modest impact on future prices. This is actually a universal effect in commodity futures. This is easy to deomonstrate if we consider a long duration between contract months.

The price of oil today has little impact on what the 5-year future does. Which makes sense. Near term drivers of oil could be weather, refinery outages, shipping logistics, and the current economy. Longer term, oil prices depend on drilling projects, regulations, and the state of economy which is anyone’s guess from our current seat. A price spike today, can lead to more investment in oil, which would increase supply in the future. Nobody thinks that a near term squeeze should have an equal response in the deferred month.

The quantitive observation that deferred months have lower realized than near months is called the Samuelson effect. Stated otherwise, contracts become more volatile as expiry approaches

💡This is a strong effect as a contract travels from being a 12 month contract to a 1 month contract but effect is smaller as a contract goes from being 10-years to 9-year or from 20 days to 1 day. The schedule of how variance decreases as DTE increases looks like a curve. Hold this thought.

The stronger the Samuelson effect, the more downward sloping you’d expect the term structure. The fact that the deferred months are only slightly lower vol and the curve is flat actually implies an ascending term structure if you adjusted for Samuelson effect.

The schedule of how Samuelson unfolds has a tremendous impact on what you believe the term structure actually says. If there was zero Samuelson effect, then the term structure you see is the actual term structure which you are then free to extract forward vols from. That’s the case of equities where all the options are struck on the same underlying as opposed to each expiry referencing a different deferred future.

The stronger the Samuelson effect, the more true term structure and forward vols ascend. If your 1 year future trades at the same implied vol as your 1 month future despite the fact that the 1 year future is moving less, means that the market is implying more variance in the coming months. If there was no Samuelson effect than you’d assume a flat forward vol not an ascending one.

Armed with this knowledge, I present the UNG vols.

The bottom panel shows UNG vols ascending thru 2025, not descending like the futures options were.

UNG options are struck on a single underlying just like regular equity options, but that underlying ETF maintains exposure to the front month natural gas futures.

In the futures options, the January expiry references a deferred future and expires in December. It is an option that references a contract that will not be moving very much for the next few months, but will be whipping around like crazy near the end of its life.

The January UNG option is referencing a prompt future that moves around a lot and will converge to the futures option in the month of December when the ETF is holding the same contract January futures option references.

The key to translating the futures options vol into a UNG equivalent vol is a schedule for the Samuelson effect. This creates a model that allows market makers to relative value trade the futures options vols vs the ETF vols. (This was central to my strategy which required normalizing commodity vols into something that can be coherently compared to other vol surfaces).

Some food for thought:

✔️Instead of designating a Samuelson schedule, you can invert the problem. What Samuelson schedule needs to be true to make futures options and UNG options be relatively in-line?

✔️How does that schedule compared to how vol unfolded in prior years?

✔️In what ways is the fundamental context of this year different from prior years?

I’ll close this section with one more picture.

That is the forward vol matrix from UNG courtesy of moontower.ai on 2/4/2025

Recall this chart:

Winter vols average in the low 50s. The forward implied vols are pricing upper 50s. That is a normal premium and if you track the forward vols every day you’ll notice that winter vols 6-12 months out will price somewhere between mid 50s to mid 60s in the case that the upcoming winter supplies look tight.

💡Winter volatility is right-skewed so if the realized avergaes low 50s the median can be assumed to be lower but sometimes the vol is much higher than the 50s. You can see the “polar vortex” in Feb 2014. You can also see just how low the vol can be in the winter:

That chart shows how deferred forward vols are like fair point spreads but have giant error bars compared to the range of realized outcomes.

 

Additional thoughts

✔️Circling back to the question that launched the post: why was the VRP (ratio of IV to realized vol) so low on January 28th?

Like looking at VRPs after earnings it’s an instance of a VRP failure mode — you are comparing a forward-looking numerator to a backwards-looking denominator. As we change seasons, nobody expects the recent bout of volatility to repeat in the next month.

✔️An example of a trade I did in the mid 2010s

I don’t remeber the exact year but in the early spring, summer vols were getting smashed as producers were selling calls as part of large hedge programs, They were bombing summer call strips. For example, if they sell 5,000 J-V $5 calls they are selling 5,000 calls in each of April, May, June, July, Sep, Oct.

30k call options in total.

I don’t remember how many total calls were sold or how long the program lasted but at some point the vols looked quite tasty.

I eyed July 4 calls which a broker was offering for 10 ticks. 10 ticks = 1 penny. So to breakeven gas had to go to $4.01

A natural gas tick is worth $10 so each option cost $100. I bought 10k for $1mm of premium. Gas was trading in the low $3 range at the time. I decided the best way to manage the trade was to risk budget it instead of delta hedge it. The options were a very cheap vol but I didn’t want to invite the path risk of selling deltas on a grinding rally where a summer risk premium started to emerge if it was looking like a hot season. Instead, I would play for a spikier move. I remember pulling up some historical charts and figuring based on an admittedly low sample size that the chance was somewhere around 20% but if it happened I’d conservatively make 9-1 on the calls. I also asked some sell-siders about whether there was anything in the fundamental context that differentiated this year from prior years.

[There’s a concept I call “analog” years where some years look like others. “In 2007 corn plantings were at this stage by this time of year and everyone thought that summer was going to be hot and the vol surface liked like this”, etc.

I didn’t check on these things so much to ideate a trade as to just check if I was missing something baked into the common knowledge the underlying market when I’m reacting to a trade.]

All told, it was reasonable to risk $1mm in premium, all-or-nothing.

So did the calls hit?

No. But, I was right about the vols being low. It was still early spring and the futures weren’t going anywhere, but the calls stayed penny bid for the next month. A month elapses, spot goes nowhere which means the IV on the strike clearly increased.

From there I had choices, I could re-asses if I thought the vol was still cheap. If not I could roll the calls up, or sell some closer-to-ATM vols and still be long vol-of-vol. If I thought the vol was still seasonally cheap, I could roll them down and have more gamma as the futures started to roll up the Samuelson curve (ie move around more). The point is there was a new set of decisions but they have nothing to do with the original trade which was “buy the cheap vol, decide how to manage it”.

In the end I was right but didn’t make a sum of money that stands out in my memory. This is not especially unusual. Trading be like that.

Extensions to think about

✔️Earnings seasonality

Market-maker’s starting point for thinking about earnings straddles will be:

1. How much has the stock moved on prior earnings dates
2. How was the earnings straddle priced going into those dates

I expect they also consider earnings seasonality. If a retailer makes most of its money in Q4 then the process for pricing earnings won’t be uniform every quarter. The sample size of relevant earnings history will be even smaller as each year maybe there’s only 1 day that is a true analog for appreciating how many days of volatility should be baked into the earnings straddle.

I’d totally expect that the market handles this well. I’m just relating the idea of seasonal volatility to assets outside commodities.

✔️Ags and softs

It’s not surprising that I took the nat gas framework and pointed it at cotton, cocoa, sugar, coffee, soybeans, corn, and wheat. Each of these markets has its own idiosyncrasies. Examples:

• peculiar option to future expiry mapping
• seasonality drivers
• concepts like “old crop” vs “new crop” which means Samuelson curves are discontinuous
• import/export features => currency correlation considerations
• unique natural flows

As a vol trader you are doing some mix of modeling and qualitative adjustments to estimate the implied forward vols in these markets.

💡It’s critical to understand how the distribution of variables that roll up to those numbers effect how the forward vol estimates are distributed…the weaker you think the Samuelson effect is the more you will be inclined to buy time spreads. Are you buying time spreads while your modeling of Samuelson is on the low end of its range? Then realize that your position is more vulnerable to near term stress than your headline greeks would suggest.

If you use percentiles to measure skew, vol or any other metric are you conditioning them on season?

Would it make sense to condition on the degree of backwardation or contango in the market?

Ok, I’m going to leave it there.

If you are interested in commodity vol stuff either directly or just to expand your own option-thinking toolbox check out:

• What Equity Option Traders Can Learn From Commodity Options (13 min read)
• Crossing The Commodity Chasm (13 min read)
• Financial Hacking: ETF vs Negative Oil Futures (a step-by-step explorable)