This is a fun one.

A good friend and mentor from the pit sent me this (lightly edited and hyperlinked):

I was catching up on moontowers and reading your cotton story. Made me think of one that you can use if you ever cover interest rates.

I started in trading with silver options. I was quite meek as I had never clerked. I was just backed and thrown in the pit at age 22. Anyway, a couple of years in, silver had rallied from around $4 to $7. The whole pit was short long dated $4.50 calls to a spec who was holding the long. These things were easily exercisable as interest rates were high. Great short to have.

Broker [badge redacted] (you may remember him) offered the synthetic put at zero. No one knew what he was doing. I bid 2 ticks under and he said sold.

So I said “1000”. I think the biggest trade in that pit was like 200.

Anyway I took 1000, exercised them and made 10 grand before commissions. The carry was probably north of 50 ticks and he increased his shorts by around 800 as all the other locals got hit with my exercises. The other locals were pissed.

So I came in through a broker and bid 2 ticks under the next day. Locals hit me. I got lucky because I was clearing [redacted prime broker] and they neglected to put in my exercise. They delayed it by mistake (and gave me the interest as I recall.)

Anyway the locals thought they found someone who would hold these things and just wanted a synthetic put for a credit. I kept doing the trade for a week.

[Redacted broker] got it right by the second day. I think I made another 5 or 10 grand before the locals figured it out and stopped doing it.

Anyway. I hope if you relay this no former silver option traders subscribe. They still don’t know it was me!

 

There’s a lot going on here!

Option pricing mechanics, pit dynamics, deduction.

Let’s start with the option pricing.

I don’t want to deny you the opportunity to figure that part out for yourself.

In the following list, I’ll start with important clarifications but as the list unfolds the material is more of a hint than just reference information.

Like a quiz show, buzz when you understand why “locals” [ie the other traders] were willing to” sell 2 cents under” and why my friend was willing to buy that level.

Clarification and hints…

• 1 silver option references 1 silver future. This is typical in commodities whereas equity traders are used to an option having a multiplier of 100
• 1 silver future references 5,000 troy ounces of silver. So if silver is $10 an oz, it’s a $50,000 contract
• The minimum increment, or “tick”, in silver options is .001 or 1/10th of penny. Since it references a 5,000 oz contract, a penny is worth $50 and a tick is worth $5.
• This story happened many years ago. Look at those silver prices: “Silver had rallied from around $4 to $7. The whole pit was short long dated $4.50 calls to a spec who was holding the long.”
• Silver options are American-style meaning you can exercise them anytime.
• “Random assignment”: when an option is exercised, any contract in that series held short is equally likely to be assigned regardless of the clearing firm or account. See rules.
• When a broker quotes a “synthetic put” (and yes synthetics are not just identities but directly traded orders!) the convention is to bid or offer as a “differential to intrinsic value”. When my friend bid “2 ticks under”, it’s understood that he’s willing to pay 2 ticks under “intrinsic value”. If the futures are $7 and the broker sells the $4.50 call 2 ticks under than the trade package is:
  • broker sells the $4.50 call at $2.498 to my friend
  • brokers buys the future for $7.00 from my friend
  • Make sure you understand this: to buy a synthetic put it to buy call and sell the future “1-to-1” (meaning for every option you buy, you sell 1 future.) Another way to express that is you hedge on a 100 delta. A synthetic put is assumed by everyone to be a simultaneous package of “long call, short future” in the same way as a straddle is call + put on the same strike or strangle is call + put on different strikes. “Synthetic put” is a real tradeable thing not just the name for an option identity.
• While futures are subject to initial and maintenance margin, option premiums are settled in full. In other words, the premium is not itself marginable. That is normal but worth stating because there are some option markets where the premium is marginable (ie WTI options on ICE)

At this point, you should be able to understand my friend’s side of the trade. If you don’t want to bother, stick around, I’ll spell it out soon enough but also that part should feel really obvious to anyone that’s ever owned an American option.

The harder question is:

Why were the broker and the other locals willing to sell him the synthetic put 2 ticks under?

Your last hint is a line already tucked into the story:

The whole pit was short long dated $4.50 calls to a spec who was holding the long. These things were easily exercisable as interest rates were high. Great short to have.

This is fun stuff. Let’s unpack it.

Why did my friend buy the synthetic put 2 ticks under?

It’s an American-style option. He buys the $4.50 call for $2.498 and sells the future at $7.00.

He exercises the call immediately, effectively paying $6.998 closing out the future he sold at $7.00. He makes 2 ticks or $10 actual dollars x 1,000 contracts. $10k profit (before exchange fees which probably claimed ~ 25% of that). Call it $7,500 for a minute’s work and no risk.

How could my friend’s buy be so good if he also says:

The whole pit was short long dated $4.50 calls to a spec who was holding the long. These things were easily exercisable as interest rates were high. Great short to have.

The key:

The carry was probably north of 50 ticks

50 ticks = 5 cents

In other words, the interest on $2.50 of intrinsic option premium was 5 cents or about 2%

💡While a market-maker will be hedged with futures, you only need to post margin to maintain that leg. You can satisfy the collateral requirement with T-Bills, so you really are capturing the the interest on the short option premium without having it offset by hedge funding which is close to zero.

💡In the story, there’s 5 cents of carry. If we knew the DTE, we could back out the interest rate prevailing back then. If we knew the interest rate, we could back out the DTE. But we have neither. We just have the recollection that the call had about 50 ticks of carry.

Think of the typical local’s position:

The whole pit was short long dated $4.50 calls to a spec who was holding the long.

The locals are hedged. They are short the deep in-the-money calls and long futures against them on a 100 delta. In other words, they are short synthetic puts. The puts on that strike are worthless however if the spec never exercises the calls, the locals will get about 50 ticks of interest. It’s like selling a worthless put for a nickel.

💡If you’re so Taleb-pilled you can’t imagine a put being worthless, just pretend you could buy the actual $4.50 put for a tick or the $4.75 put for 3 ticks. There’s such a thing as arbitrage bounds. Options 101 stuff.

Amateurs will say things like “that’s worthless” because they believe a price “can’t get there” but when I say it’s worthless I mean by arbitrage. Like the value of the put on that strike is dominated in such a way that if you could sell it at a positive value there’s free money on the board. An option trader thinks in a matrix of arbitrage relationships when they examine a chain.

You can see why the locals were willing to sell the put 2 ticks under. They didn’t think they would get assigned! They assumed they were going to collect 50 ticks on a riskless position.

The mistake was in thinking my friend wouldn’t exercise the calls. Perhaps they thought he needed to cover risk and if they were all short the calls he was just closing. But that doesn’t make sense to me since he was a “meek” trader before then and certainly wouldn’t have been short 1000 calls.

That’s the most puzzling part to me. I understand why they might believe a customer like the spec would not exercise the call optimally, but when a market-maker buys them you need to update. “This guy who trades options all day is buying an American-style option below intrinsic, I wonder what he’s going to do?”

I don’t want to be too snarky because “street smart” is probably one of the most salient features of a pit trader. I’ll assume I’m missing a detail that makes their decision justifiable.

 

The rude awakening

“The other locals got hit with my exercises. The other locals were pissed.”

This is the random assignment. When my friend exercised his calls the free interest gravy train slowed down as suddenly some of the locals got assigned which closed their positions (the short call goes away and the long future they were hedged with is liquidated to the exerciser).

💡In random assignment, you “expect” to be assigned on your pro-rata portion of the OI held by all shorts. How many you actually get assigned on can vary from this theoretical expectation because the sequential 1 by 1 assignment process is memoryless just like dealing from a deck of cards with replacement each time. Just because you got tagged on the last one doesn’t change your odds of getting tagged on the next one.

Let’s keep unpacking the story.

Poisoning the well

My friend masked his behavior to blend in with customers and used a broker to “bid 2 ticks under” the next day. The locals didn’t think it was a market-maker going through a broker. The locals were reasonable in not suspecting a local to be hiding themselves behind a broker order for 2 reasons:

1. Paying commission which would eat into the slim margin even further.
2. This behavior is known as “poisoning the well”. This type of pro vs pro crime was considered bad form. Just like in poker how the pros try to avoid each other and just eat the fish. Of course from the outside, the norm is considered anti-competitive.

Let’s address both of these.

Regarding #1:

My friend may have worked out a deal with the broker. After all, the broker stands to make a thousand bucks or so for no real effort and if the order is contingent on a reduced commission rate they’ll probably go for it.

[I used to do this all the time. Wet the brokers’ beak. We like to talk about nerd stuff and math here, but trading is a business like any other business. Giving out orders is currency. Traders who pay lots of commission magically get the first call. Whether it’s commodities or equities brokers can solicit the other side rather than bring an order to the pit and instead just cross it without worrying about the order being broken up (ie bettered) they can double-bill. Brokers are fiduciaries and their business is competitive, get too many bad fills and you risk losing a customer, but there’s a lot of leeway in discretion. I’m using a broad brush, the rules and details vary across asset classes, but the mechanics rhyme everywhere.]

Regarding #2:

Prisoner’s dilemma.

How much is it worth to defect?

Will we return to stasis and you got away with one or did you really poison the well?

Will anyone find out?

Does any of this change if you don’t really fit in with the club and can’t hope to be part of it?

And then there’s pure disagreeability mixed with self-confidence. I was at Max’s soccer game last weekend and the ref in a moment of deprecating humor said “They told me when I was a kid you need to either be smart or likeable. And I’m definitely not smart”. I don’t think this particular buddy ever cared about going along to get along. But he’s also super-smart.

I’ll add my own perspective to the game theory stuff. I did nothing but watch markets get tighter, more competitive and more ruthless over time. The edge you never would have settled for becomes something you’d kick grandma down the stairs for before you know it. Someone is going to defect.*

This is chained to another observation. In a landscape where there’s excess profit (ie too much reward per unit if risk) there is always someone sandbaggin’. They aren’t showing how smart or fast they are because they will harvest at this level before it tightens and not have to tip off to others what’s possible. I know this firsthand because of a friend that runs a brilliant trading operation in a niche space in which he never shows the market how fast he really is. Imagine my lack of surprise when I read about this “don’t show” tactic from HFT-er Liquidity Goblin’s Let’s Pretend We Have An Edge (paywalled).

A fortunate mistake

I got lucky because I was clearing [redacted prime broker] and they neglected to put in my exercise. They delayed it by mistake (and gave me the interest as I recall.)

Anyway the locals thought they found someone who would hold these things and just wanted a synthetic put for a credit. I kept doing the trade for a week.

[Redacted broker] got it right by the second day. I think I made another 5 or 10 grand before the locals figured it out and stopped doing it.

My friend was able to milk the ruse for a bit longer because of an error! The prime broker failed to process the exercise which reassured the locals briefly that they were not getting picked off. Sounds like it gave him at least another day to buy more synthetic puts for a credit before the locals got wise to the game.

Knowing is half the battle

Let’s put a bow on this like an 80s cartoon ending lesson.

Being short those synthetics to a single counterparty who doesn’t realize the calls should be exercised is good fortune. But once someone wants to buy those deep ITM calls opening, you know that they know what they’re doing.

I’ll tell you from personal experience that anytime someone wants to trade a deep option or a reversal/conversion where there is little or no open interest your guard goes up. You check your funding assumptions. You think harder about what your option model is saying about the value of an American vs European style rev/con. The difference between the 2 represents the value of the early exercise option for that strike. Those are modeled via trees simulations and difficult to debug as opposed to closed form equations for European Black-Scholes.

Only the paranoid survive.

---

 

*I refer you to this excerpt from A Former Market Maker’s Perception of PFOF:

SIG wasn’t know as the “evil empire” on the Amex just because of the black jackets we wore. They understood the risk-reward was completely outsized to what it should be 25 years ago. They were amongst the first to tighten markets to steal market share. They accepted slightly worse risk-reward per trade but for way more absolute dollars. They then used the cash to scale more broadly. This allowed them to “get a look on everything”. Which means you can price and hedge even tighter. Which means you can re-invest at a yet faster rate. Now you are blowing away less coordinated competitors who were quite content to earn their hundreds of percent a year and retire early once the markets got too tight for them to compete.

SIG was playing the long game. The parallels to big tech write themselves. A few firms who bet big on the right markets start printing cash. This kicks off the flywheel:

Provide better product –> increase market share –> harvest proprietary data. Circle back to start.

The lead over your competitors compounds. Competitors die off. They call you a monopoly.

Recently, I’ve been writing a lot about option funding — implied rates, reversal/conversions, and financing stock positions, and even a touch on early exercise. The posts from earliest to most recent:

• the easiest win in options is for stock traders
• implying the cost of carry in options
• what hides in the option chain
• the art of paranoia

You can’t really overstate how important this is, especially to pros.

On the same theme, Stanford lecturer and HF manager Kevin Mak published an outstanding and detailed post:

Holding a high cost to borrow stock? Here’s how to collect the borrow fees using the options market (link)

I want to quote a few key parts:

I cannot stress enough that if you want to be competitive in capital markets, you cannot afford to make these types of mistakes and forgo this return.

Kevin is quite blunt:

If you think this is too complicated to follow, to be blunt, you likely do not have the mental fortitude to have alpha in markets (you may still make money via luck). If you CAN figure this out, but couldn’t be bothered to spend time on it, that’s probably fine, but I suggest staying away from holding a stock with a high cost to borrow. If you insist on holding high cost to borrow stocks, and “not worry” about collecting the free borrow/lending fees, you really should be playing triple-zero roulette, or splitting every pair of 10’s at Caesar’s Palace instead because that would have a lower edge, and be way more fun.

I suggest that by using options to refinance your position, you “inherit the market maker’s funding rates” which are almost certainly better than yours, whether you are long or short.

This is Kevin’s way of saying this which might land better for some (emphasis mine):

If this is arbitrage, it shouldn’t exist right? This unique situation is you “arbitraging” your own holdings. You’re basically holding an inefficient asset since you can’t lend it (or collect the lending fees) so this lets you own it in a more efficient manner. Nobody is going to compete away this arbitrage because nobody can access your holdings except you. In fact, it’s the arbitrage happening in the open markets which is pushing the value of synthetic long to be equal to the long stock (and collect borrow) position.

Kevin wisely tucks all the brain damage into the endnotes to not ruin the flow and central message of the post. I love his intro to them:

This is a beginner treatise on a synthetic long position and covers ~98% of what you need to know about it. The last 2% I could write 25,000 words about and not be finished.

In the spirit of the endnotes, I want to share a recent real-world example of a scenario that resides in that annoying “2%”

Alex, a mutual of mine on X, asked the following:

I bought some deep itm $AIV calls, I think Jan exp, a couple weeks ago because I thought they were cheap vs my financing cost. Not much extrinsic value… Underlying had silly spike after hours, up then down.

Was the right way to trade this, to short the underlying after hours? I thought about exercising to sell, but didn’t want to burn a few months of time value for nothing, even if I didn’t really pay for it.

I’m going to step through the conversation, injecting meta-commentary to bring it down a level.

Me: Your trade expression was because of financing but you are asking about what you should have done with your delta. I’m not being pushy, I’m just trying to help you answer your own question.

There are 2 things I can see so far:

• Alex is conflating his strategic financing decision with tactical delta management. I do the Socrates thing as a habit when learners entangle multiple issues into a single question. If I just jump ahead and answer each part of the implied questions, I rob Alex of a valuable opportunity — to debug his own thinking by breaking the big question into its components. I notice many people getting option or trading concepts rolled into a ball of yarn, which tells me they don’t understand each string as well as they should. When you’re forced to decompose your own question, the deficiency is self-apparent.
• He’s showing good instincts about not wanting to exercise the calls because he’d be “burning a few months of time value.”

💡Option Pricing Clarifications

1. The first [but not final] check on whether you should exercise a call is if the value of the OTM option on the strike is worth more or less than the cost of carry.
   1. For an ITM call, is the dividend you are exercising for worth more than the put on the same strike?
   2. For an ITM put, is the interest on the stock short if you exercise greater than the call on the same strike?
2. Alex said he thought about “exercising to sell,” but to be clear, you can’t exercise the calls after-hours and have it settle the next day. There is a cut-off for exercise notices. He would have needed to short the stock after hours, then exercise the next day, meaning he would have to carry a short for 1 day. This tactic would have flattened his delta, but he would have to incur any financing ramifications for the 1-day short.

This simple scenario highlights a risk to using heavily-discounted synthetic futures to express a long:

If you plan on liquidating the length before expiration, you are exposing yourself to the change in funding that you otherwise locked in.

In this case, Alex is exposed to the borrow he may have to pay on short shares if he chooses that route to cut length. One day’s borrow, even if steep, is unlikely to make or break the whole trade, but the bigger issue is the “locate”. There might not be any shares to borrow from your broker. If Alex was long the stock instead of the synthetic stock, he could just sell it in the after-market.

If Alex chooses to cut length by selling the ITM call, it may be for the same discount that attracted him to buying them in the first place. It’s like buying a home for a discount because it has lots of street noise. It’s a problem you can’t outrun because you will be on the losing end of the discount when you sell the house.*

Stay groovy

☮️

 

*Tangential, but I see people misunderstand this in the private school vs public school debate. If you pay up to live in a good school district, you are exposed to 2 risks:

1. The carry cost on the premium. If you pay 20% more for a good school district, the funding cost on the extra ~20% of mortgage is the cost. If schools are the deciding factor between an $800k or $1mm house and mortgage rates are 5% then your pre-tax cost of the better schools is ~$10k per year. This is probably much less than private school tuition, especially if you have multiple kids.
2. The perception of school quality. The “school premium” can expand or contract over time. You can win or lose to this when you sell.

In general, the true cost of the premium you pay for good school districts is very small relative to private school tuition, making your VORP hurdle for private school choice high (although worth it for many people).

Here’s an FYI that reinforces a lot of moontower 2025 writing on option synthetic futures.

This is from my IBKR screens from 10/22:

Spot VIX was 18.4

I highlighted the March VIX future. It had a mid-market of 21.725

The ATM strike for options on VIX expiring in March is 22.

The combo or price of the 22 synthetic =

call price – put price = 3.50 – 3.78 = -.28

Synthetic future = Strike + Combo = 22 -.28 = 21.72

No arbitrage available folks (as expected).

The synthetic future on VIX and the actual VIX futures trade in line.

💡The VIX options and futures typically expire on the Wednesday morning preceding monthly option expiry cycles. The options cannot be traded between the prior night's close and the Wednesday settlment but the futures can.

We’ve been talking about option funding stuff recently in the paid Thursday issues. Recently, I had a trader ask for some help making sense of an option expiry in a single name that trades by appointment but where some chunky size goes through.

It’s a name with lots of hair on it with respect to events and distribution.

[The current mark of a big option trade that went through a few weeks ago is still rattling in my head. I’m looking forward to where the roulette wheel is gonna land on this thing!]

I’m obviously not going to give away the name, but I can recycle some of what I explained to the client using a fake stock.

It’s rooted in funding and why understanding it is frankly critical for making sense of names that have wide markets. You’ll see :

• the first thing that caught my eye when I looked at the option chain
• put-call parity’s relationship to a vol curve
• how to avoid making really dumb trades (or if you’re a broker how to look like a hero to your client)

We can do this with screenshots and commentary to make this tour brisk but rich.

We begin with an invented option chain for our fake stock. I chose these values to be in keeping with the quality of the real stock’s markets without giving anything away.

For any junior traders or trainees this is good diagnostic practice — to eyeball an option chain and take notice of what’s interesting.

Relevant background info:

✅European-style expiry (it’s complicated enough without early exercise)
✅No dividends
✅RFR: 4%
✅DTE: 43
✅Stock price: $108.50

What do you notice:

Don’t start all nerd mastermind. Instead observe. These markets are wide!

Well, before you start thinking “The 125/130/135 call fly is negative, yay free money”, you should recognize that the market widths are obscuring this vol surface. I mean, if you think you can trade at mid-market, there’s free money all over this board. All kinds of bells should be going off but just as a surgeon has a checklist, there is definitely a priority thing to look for.

Think a bit before I offer a hint.

 

Ok, here are 2 columns that should help:

IVM = “IV Mid”

Categorically, the call IVs are greater than the put IVs on the same strike.

 

It’s safe to assume the stock is $108.50 as I indicated in the setup.

So what’s the likely culprit?

The rate.

We used RFR = 4% but with that rate put/call parity is not holding.

This is messy since we are using the mid of wide markets, but I didn’t contrive this situation from scratch— it is based on a real snapshot the client showed me on a screenshare, so it’s an opportunity to address real-world complications.

If call IVs is categorically higher than put IVs then the IV is being computed from a rate that is too low.

Instead of imposing a rate, let’s try something else. We will require that put/call parity hold at each strike.

💡Review the method: implying the cost of carry in options

This table is a handy way to start:

I highlighted the 110-strike because it’s closest to the $108.50 spot price.

The right-most column shows the implied yield of each strike. By computing an implied yield the call and put IVs are forced to be the same but I left the stale ones in the table for the sake of this chart:

It demonstrates that a difference in call and put IVs is another way of saying the implied yield or cost of carry on each strike is different.

If you impose put/call parity, forcing the IVs on the strikes to be the same (I didn’t recompute the IVs on each strike here with the implied rates from their strike), then instead of seeing a chart with call and put IVs not lining up you’ll get some implied rate curve across strikes like you see here.

Let’s look at this like a checklist:

✔️If the call and put IVs differ across the strikes when imposing a cost-of-carry parameter (as we did with 4%) then the market is telling you your cost-of-carry parameter is wrong.

✔️Instead, impose a market-based yield by starting with the no-arbitrage assumption of put/call parity to get call and put IVs to line up.

✔️But if this leads to large disparities in implied rates across strikes, well, we still have a puzzle.

Looking at our rate curve…we still have a puzzle.

Experienced traders know why, but just to bring it along gradually, here’s another table that will look very familiar to anyone with an ETF, index, or options arbitrage background:

Computing the implied market by calculating the implied synthetic stock futures bid and offer.

Remember, the synthetic is just the combo price (c-p) plus the strike price. In the prior table we based our synthetic prices on the midmarket values of the options.

Here we want more detail. For each strike, we calculate:

synthetic bid = call bid – put offer

Take the 110-strike as an example to consider what this means…if you hit the screen bid on the calls AND simultaneously lifted the screen offer on the puts, effectively crossing 2 $3 wide markets (before you got fired), you have sold the synthetic future at $107.

We compute the implied yield bid/ask using the implied combo bid and offer with the same logic. [Again, to turn option combo prices into implied yields see this post.]

The puzzle as to why we are getting a ridiculous range of implied yields is not too mysterious — the markets are just too wide. Garbage.

We will do our best with what we have because there’s still plenty to see.

The art of computing the vol surface

The preferred way to set a vol curve is to imply the rate, then impose that on the surface to generate strike vols. Since the implied rate on each strike based on mid-market won’t be perfectly uniform (although likely much better than this stock) you will still get different call and put IVs on the same strike but they are not likely to “cross”. In other words, you won’t be able to lift a call option on a strike for a lower IV than you can sell on the put (or vice versa). The error in IV should be within the market widths.

To give you a flavor of how you impose an implied rate on the strikes across the same expiry we can consider a few methods.

The tightest market

We cobble together the best bid and offer from any of the strikes to imply a yield. I don’t love this method for actually estimating the rate, but it’s the fastest way to spot an arb! Look at all the implied rates…the 75 strike really sticks out like sore thumb. If you hit the call bid and lift the put offer you have synthetically sold the stock at $109.80. If you buy the shares for $108.50, borrowing to finance them until expiry in 43 days, you will have legged a “conversion” trade for a fat profit.

Trader math — I borrow $108.50 for 2 months at 5% (notice conservative assumptions on both days and rate) that’s 1/6 * 5% or 80bps on $108…call it 90 cents. So I buy stock for $108.50, sell it at $109.80 and pay $.90 in interest…$.40 pure profit. Manage to get filled on 50 combos? That’s $2k in 2 seconds. Annualize that.

I’m getting carried away. This kinda thing is never just sitting there because it’s easy to program a bot to “eye” for it and then if it does find it, it’s because you ingested stale data. Still, I hope I conveyed the benefit of the “tightest market” method even if the benefit accrues to speed demons.

Weightings

How else can we find an implied rate to impose across all strikes? We could average the implied yields we find at each strike but give more weight to strikes with tighter markets (in this case, every market is $3 wide so the strikes would get equal weight and given the widths — still garbage).

We can just choose to look at a range of strikes near-the-money. We can weight their implied rates by inverse distance to the stock price. We can exponentially weight tight markets. We can draw hard cutoffs on strikes that exceed specified widths. You can use a solver across strikes but even then you probably filter the strikes according to criteria that come from experience.

[And when it comes to American options, may god have have mercy on our souls. The value of rev/cons can vary widely across strikes as the probability of early exercise differs. You are very much triangulating across several unknowns because the probability of an option being exercised also depends on its vol so you end up falling back on some ordinal relationships that bound early exercise relativity between strikes. In English, it’s easier to say relative things about early exercise adjustments to rev/cons than it is to absolutely value a rev/con. If there’s one area that even experienced traders trip up on its American options. Through the grapevine, from multiple sources, I’ve heard that one of the largest market makers in the biz lost a meaningful proportion of their annual profits because their mispricing of early exercise was exposed during the rate hikes in 2022.]

Anyway, there are enough choices involved that no 2 firms compute vol surfaces starting with implied rates in exactly the same way. There’s no benefit to bogging down on a specific method for this post so I’m just going to impose the 11.65% rate from the 110-strike and re-compute IVs.

With the single rate, the call and put IVs come closer together especially for the near-the-money options. The deep OTM options are going to stay a problem because a $3 wide market on a .15 delta option is just a lot of vol points of noise. [The vega on those options is much smaller than ATM, so $3 represents more vol width.]

Towards a single vol curve

Usually when you look at a surface, it’s just a single vol curve through all the strikes for a given expiry. A common way to do this is to simply use the IV from the OTM option. That option tends to have a tighter bid/ask width since it has less delta risk for the quote streamer.

If you don’t want to dismiss all the information from the ITM option on the strike, you could weight the IV inversely to the market widths or even to the options’ contribution to the straddle price on the strike. Here’s the vol curves using the OTM method and the Inverse Contribution To Straddle method:

Looks like a “W”.

If you have been paying attention to all the stuff I’ve written about vertical spreads and butterflies, you can guess the implied distribution:

bimodal

And yes, the original stock I helped the client with does indeed look bimodal. This is also a distribution you often see on stock earnings.

[My group used to call it the “teepee” and I heard from some transplants that it was another famous market maker who made a lot of money “teaching” the market that this was the right shape for a vol surface in particular situations.]

While this fake stock is the spawn of a real bimodal stock, this is not the most interesting thing about the surface.

By far the most important thing to see is that the implied rates are totally jacked!!! The calls are leaned incredibly high relative to the puts. You have to be able to see this right away (or infer it from the call IVs being high relative to the put IVs if you use a platform that doesn’t impose put/call parity on ATM mid vols).

Calls should never be too high relative to puts because conversions are easy arbitrages especially in non-dividend-paying stocks.

[In conversion trades, you sell call, buy put, buy stock. You must fund the stock purchase so you are exposed to rising interest rates. But that is the only material risk.

Reversals which entail buying call, shorting puts and shorting stock are exposed to declining rates but also any suprise dividends or the stock becoming harder-to-borrow. That’s why you almost never see implied rates trade much higher than SOFR — it’s easy to arbitrage via conversions. But implied rates often trade far lower than SOFR because borrow is uncertain. If you do a reversal trade because you want to exploit the implied rate, your most likely outcome is to find out the rebate you anticipated on your short stock was wishful thinking].

What can you do if you notice the calls are too high relative to the puts?

The eager beaver is going to say “do a conversion arbitrage”. I appreciate the optimism. But those markets are wide. Those mid prices are fake. You can’t get filled anywhere near mid if you try to sell calls or buy puts.

But that’s the clue.

What do you do with the knowledge that the implied rate is too high if you can’t do conversion arbs?

You simply don’t buy calls or sell puts anywhere near mid-market. You are walking into a trap. If you are a broker or advising someone, you explain this to them as well. You’ll save them a bunch of money and they’ll appreciate that you know your stuff.

[This also helps manage expectations. If you are a broker and given an order to sell calls into this market, you should point out that the implied rates are high, meaning the calls are leaned up, and the customer shouldn’t expect to get filled near mid. Similarly, they wouldn’t be able to buy puts near mid either as those are leaned down.]

 

In closing, when you look at an option surface there are so many invisible decisions about how to compute the IVs. When you see call and put IVs that vary greatly, your instinct should be to imply the rate. This post has been in the recent tradition of “options are ALWAYS about vol EXCEPT when they are about funding” but I hope today’s effort has actually shown that we can’t actually compute the vols without understanding funding.

One of the funny things about options is that while variance is an abstract concept to trade (the square of standard deviation??) it’s a straightforward bet — the outcome of the trade is tied to the intent. The payoff reflects the expression. If the realized volatility will be low, sell this.

Meanwhile, listed options, literally called “vanilla”, these American-style shape shifters tradeable from your phone are a pile of path-dependent, hard-to-solve “halting” problems, being discussed by weekend-house-flipper salespeople because there are so many ways to win or lose that are unmoored to your original intent that the randomness of the experience makes them perfectly marketable despite their basics being inscrutable to their average user.

I hope this post made them a little less inscrutable to you.

This is the follow-up to last week’s the easiest win in options is for stock traders.

In that post, we started with a puzzle that leads to a critical insight:

The collective pursuit of option arbitrage means that we can use put-call parity in reverse — to imply the cost of carry instead of assuming one, THEN trying to impose put-call parity.

In the example of the $100 stock and 4% SOFR rate, we computed the cost of carry or what we formally call the “reversal/conversion” or R/C was $3.92.

synthetic future = C – P = intrinsic Value + R/C

where:

C = call value on the 100-strike

P = put value on the 100-strike

The fair value of the synthetic future in our example is therefore:

→ synthetic future = intrinsic Value + R/C

→synthetic future = (S – K) + R/C

→ synthetic future = (100-100) + 3.92 = $3.92

I expect the call to be trading for $3.92 MORE than the put on the 100-strike if the stock is $100.

If it’s trading for a larger premium than $3.92 then there should be an arb:

• Sell call, buy put [short the synthetic future]
• Buy the stock

This is a “conversion trade and since the cost to finance the long shares is the 4% we used to compute fair value, I should have a profit left over.

If the call is trading at a discount to $3.92 vs the put then I should be able to do a “reversal” arbitrage where I:

• Buy call, sell put [long the synthetic future]
• Short the stock

The interest I collect on the proceeds of the short sale should exceed the premium I paid for the synthetic.

That’s the theory.

Of course, if you’re fair value differs from market pricing, guess who’s probably wrong.

Instead of using some assumption about the cost-of-carry, we invert:

“What does the cost-of-carry need to be for put-call parity to hold?”

It’s hard to overstate how powerful this inversion is. It has profitable applications to retail option traders, directional stock traders, both long and short, quants modeling option surfaces, and even fundamental investors concerned with dividends.

Conveniently, the lowest-hanging fruit affects the largest groups — directional stock and option traders. We will cover this in detail while keeping explanations shorter for the more professional applications.

We start with a question:

Have you ever noticed that the call IV and put IV for the same strike on an option chain are NOT equal?

This is all going to make sense soon. With some basic mechanics and simple algebra we are going to discover a whole new order book for stocks.

Solving for r: volatility is not the only thing we imply

We are going to take this journey in small steps.

We start with our identities to build our “if-then” muscles:

where:

K = strike
r = risk-free rate
t = fraction of a year

If r increases, R/C increases as the gap between the strike and strike discounted to PV widens.

Let’s re-arrange the synthetic future identity which includes the R/C to be in terms of the call and put respectively:

→ Synthetic future = Intrinsic + R/C

→ C - P = (S-K) + R/C

If r increases, R/C increases, therefore, calls go up in value while puts go down in value.

The heuristic:

When interest rates are higher the opportunity cost of buying shares increases or the cost of leverage increases if you buy on margin. Arbitrage ensures these costs are passed into the value of calls just as they are passed into the basis of futures over cash in any forward market.

Volatility

The inputs to the Black Scholes pricing formula are:

• stock price
• strike price
• DTE (as fraction of a year)
• RFR
• volatility

For a given volatility, you can compute the call value, then, without using an option model, use put/call parity identities to compute the put from the call.

Note these call and put values are generated by the same volatility. We used the vol to get the call and then computed the put.

But this workflow isn’t typical. Instead, we are usually looking at option prices from a chain with implied volatility. In other words, the workflow is inverted. Instead of inputs generating option values, we see option values and imply inputs.

Notably, implied volatility.

Implied volatility is computed by fixing the option price and letting the volatility be the unknown.

[The solution is usually computed with a simple search algo like the Newton method which starts with a guess, then iterates until you are “close enough”.]

The RFR will be fixed to compute the implied vol, but when you observe the option prices you may find that the call and put have different implied vols. Another way to interpret this:

Put/call parity is not working.

But here’s the thing — put/call parity must work. If it doesn’t “work” there’s an arbitrage.

• If the call IV is lower than the put IV, you can do that reversal trade: buy call, sell put, short stock
• If the call IV is greater than the put IV, you can do the conversion: sell call, buy put, buy stock

What do you think is going to happen?

You will discover that a key assumption in the formula for generating those implied vols is wrong. The strike and DTE are in the contract specs. The stock price and option prices are observable from the marketplace.

The only variable remaining is the interest rate.

You can certainly call your broker to verify the interest rate, but they won’t be able to tell you tomorrow’s rate or any day after that.

What does this mean?

If you impose the rate and the call IV > put IV, then the market’s implied rate is lower than your assumption [and vice versa].

By assuming put/call parity must hold we are saying that the IV on the call and put of the same strike must be equal. But the only release valve for this constraint is we must accept that the market-implied rate can be different from what we think it is.

This is exactly what we should do.

By measuring the market rates by assuming no-arbitrage, we can then decide if a trade is attractive given our own funding rates. If the market implied interest rate is lower than what our broker offers (ie calls look cheap and puts look expensive or said otherwise the synthetic future looks discounted), then instead of buying the stock, we can buy the synthetic.

In fact, this is what professional option desks are doing all the time — they compare their funding costs from their brokers to the market-implied funding costs. If they can “refinance” their position in the options market, they effectively “go around” their broker. The implied funding market in options, including box rate markets, is often tighter than the spread of your broker’s long vs short rates. For a large enough desk it is not uncommon to have a trader whose entire job is to “manage funding” by trading rev/cons across the portfolio to reduce gross notional balances (ie if they are long lots of stock they will look to reverse or swap into futures if the cost of carry is cheaper than what the broker charges to borrow).

Solving for implied rate

Back to something we can easily see in the market — the price of the synthetic future (also known to older traders like myself as a “combo”):

Synthetic future = Intrinsic + R/C

C - P = (S-K) + R/C

I’ll use the examples from the webinar.

On 7/18/25, USO was trading $76.06

I pulled up the closest ATM strike in each month — the 76 line — and computed the synthetic future as the call – put.

I then subtract the intrinsic value of $.06 from each combo. The remainder is the R/C or cost of carry.

Remember:

We just rearrange this to solve for r, which gives us the implied rate.

Notice that the implied rates are below the Fed Funds curve at the time.

If you started with “I’m certain that the Fed Funds curve reflects my funding rate” then the combos would all look too cheap. When you “reversed” to do the arbitrage by buying the synthetic future and shorting the stock you’d discover why your Fed Funds assumption was faulty.

You will find that you are earning less than Fed Funds on your short stock proceeds.

But this gets better.

This is a perfect demonstration of why understanding this concept is immediately profitable. On 7/18, Interactive Brokers was charging 5.93% annualized to borrow USO. But you could short the stock via options to collect the rev/con instead of paying fees!

Consider the October expiry:

You could sell the synthetic futures at $.98 or $.91 more than intrinsic value, effectively collecting 3.3% annualized to be short USO instead of paying 5.93%. This is more than a 9% swing in carry costs (which is about 1/3 of the stock’s annual vol to put it in context).

Even though the funding rate from your broker stinks, you can “inherit” the market-makers rates by trading the options. The market-makers battling for arbitrage is a giant peace dividend to the rest of us who cannot access the same rates and borrow that institutions can. But even if you are a professional, the implied rates are often out of sync with the rates you can access, so there’s ample opportunity to refinance your positions in the synthetics market. The implied rate curve in the term structure is effectively an order book for a stock through time.

💡Refresher on how shorting works
→ If a stock is easy to borrow, you might earn a positive rebate (e.g., SOFR – 25 bps) on collateral of short proceeds
→ If the stock is hard to borrow (high demand, low supply), the rebate can be negative. This means you pay to borrow the stock (sometimes called the borrow cost)

Discussion

It should be a revelation to realize that the physical shares market is only one price for a stock, but the derivatives markets offer many others. The USO example showed how you can short USO at a higher synthetic price than if you borrowed the shares directly. Similarly, if a synthetic future trades far below the stock price, reflecting a high borrow cost, anyone who cares to buy the stock will get a massive discount in the options market.

The “real” market

When BYND went public, the peanut gallery (ie twitter) was all screaming how they wanted to short this fake meat company, but this was a consensus view — the shares were impossible to get your hands on to short. I’m going off memory, but the options market was pricing the synthetics at about ~40% discount to the ordinary shares. So the question for the peanut gallery isn’t “Do you still want to short the shares at the market-clearing price where the stock can be both bought and sold?”

Because that price is 40% lower. And if you were a long-term bull, what are you doing buying the ordinary shares? Just take the 40% discount and buy the synthetic.

[BYND has lost most of its value since it went public 6 years ago, but I wonder if a trader who but synthetic futures and rolled the position at each expiry would have actually won. I really hope so since that would be one of my favorite case-studies on the nature of trading.]

Backtesting

Directional traders who test both long and short strategies should be using the option synthetics market to reflect tradeable prices because those prices “lock in” a funding rate. Otherwise, backtests not only require borrow rate data sets but also need to deal with the fact that borrow rates change daily. A wicked backtesting concern.

Funding all the way down

In etf fair value, I mentioned an old habit from my arb days: computing the premium/discount on an ETF before trading options on it. I’ll leave this for you to ponder:

If an ETF trades 1% above its NAV, where should the synthetics on the ETF trade?

Vol modeling

When computing option surfaces, it’s common practice to imply the rate, THEN use that rate in the implied volatility formula to compute the IVs across the skew. This ensures that each strike has a single IV, and when charting the skew, we use the implied vol from the OTM option — its mid-market willbe more reliable because of narrower bid/ask. Having a single IV per strike also ensures the absolute delta of the call and put sum to 1.

In the examples I gave above, we implied the rate from a single strike that was closest to ATM. But a more robust method would average (or weighted average) the implied rate from more than 1 strike in case the bid/ask on any single strike was shaded too much in one direction. Multiple strikes would minimize the impact of those artifacts.

Dividends

I only addressed dividends in the appendix of the prior post to keep all of this a bit easier. For our current purpose, just recall that dividends decrease the cost of carry or R/C since the call owner misses out on the dividend but still experiences the stock falling by the amount of the dividend. Meanwhile, the put owner forgoes owing the dividend on the counterfactual short shares position and benefits from the stock falling by the amount of the dividend when it “goes ex”.

→The rev/con falls pushing puts up relative to calls

Easy enough.

However, the idea of an implied rate gets more complicated when we solve for r in the presence of dividends. Although it’s not hard to understand conceptually.

Consider a situation where Fed Funds (I’ve been using FF and SOFR interchangeably), is 4%, we expect the stock pays a 1% dividend, but the rev/con is 2.5% instead of something closer to 3% that we would predict from the general shortcut of cost of carry is interest – dividends.

Is this because the options market is saying your short rebate is 50 bps less than Fed Funds OR the stock’s dividend is expected to be 50 bps more than it has been in the past OR some blend of a dividend increase and rebate difference?

Do you see how incorrect assumptions here change the implied rate, which in turn affects all the implied vols?

Not only is there an implied rate, but an implied dividend. Whenever we get multiple unknowns, we need multiple lenses to triangulate. This is the realm of quantitative vol surface modeling, a task that many professional option traders outsource to specialty firms especially if their trading must discern the value of a penny in the premium.

This concludes the 2-part series on options as funding markets. As I said in part 1, this topic represents the largest gap between what people know and what they should know about options. It affects pricing, it’s highly actionable, and by allowing anyone to “refinance” a position at professional rates, it stands as one of the easiest win-wins in trading.