I should tell you where this really started, because it was not in a trading terminal. It started in childhood.
I grew up Muslim, and like every Muslim child I was taught early that riba, interest, is forbidden. Not discouraged. Forbidden, in the strongest terms a believer knows. And yet everywhere I looked, the entire financial world was built on it. Every bank, every loan, every savings account, every mortgage. The one thing my faith placed firmly outside the bounds was the exact thing modern finance was constructed from, all the way down to the foundation. As a child I could not hold both of those facts in my head at once, and the question never really left me.
What stayed with me most was the people. I watched men and women around me who prayed five times a day, who fasted, who feared God and would not knowingly eat what was forbidden, live their entire financial lives inside the interest-based system anyway. Not because they did not care. Because there was no alternative. You cannot buy a home, run a business, or keep your savings from inflation without touching the machine, and the machine runs on riba. The prohibition was clear. The way out did not exist. Good people made a quiet peace with a contradiction because no one had ever built them another door.
Somewhere in there a conviction settled in me that I have not been able to shake since: if God forbade something, there must be a way to live and to build without it. Not a relabeling. Not a legal costume stitched over the same interest underneath, which is most of what passes for Islamic finance today. A real alternative. And as I grew into a finance professional, that conviction hardened into something closer to a duty. If I could see the problem clearly and had the tools to work on it, then the work was mine to do.
So I became a trader. I taught myself in Dhaka, mostly alone, over years when there was no community to ask and no infrastructure to lean on. When I needed market data and there was no API, I automated a browser to scrape it. When I needed a modern stack, I learned it from documentation by myself. I learned the hard way too, losing most of what I had on a single leveraged trade, that conviction is not a system. I tell you this only so you know I came at finance from inside the machine, not from a seminar.
And the old childhood question followed me in. Every system I built, someone would eventually ask: is this halal? The honest answer kept coming back no, or not cleanly. To trade with leverage you use perpetual futures, and perpetual futures charge interest, and that interest is riba. The very thing I had wanted to escape since I was a boy was sitting inside the instrument I used every day.
The night the interest was missing
Here is the one piece of background you need if you do not trade crypto. A perpetual future is a contract that lets you hold a position on a price, say gold, with no expiry date. Because it never settles, it can drift away from the real price. So exchanges use a payment called funding, exchanged every few hours between the two sides of the trade, to keep the contract tethered to reality.
I was reading how exchanges compute that funding. On Binance, the formula has two parts. One is the premium: simply how far the contract has drifted from the real price. The other is a small fixed interest rate, added regardless of anything: the 0.01% Binance applies every eight hours, which works out to roughly eleven percent a year, charged just for holding a position over time. That second part is the riba.
Then I looked at dYdX, one of the larger decentralized exchanges, in its fourth version. And the interest term was gone. Not hidden, not renamed. Gone. Their funding is only the premium: the gap between the contract price and the real price, divided by the real price. Their interest-rate term is set to zero by default. Payments flow back and forth between the two sides depending on which way the contract has drifted. Sometimes you pay. Sometimes you are paid. Sometimes nothing changes hands.
I sat with that, because it was strange. Here was a real exchange, real money, real scale, running the same instrument as Binance, and it had quietly removed the interest. And nothing broke. The market still worked.
That is when the thought arrived, the one that turned a trading problem into three years of work: if a working market can price this with no interest, then the interest was never necessary. It was a choice. And if it can be removed here, where else?
What follows are the questions people have asked me ever since, including the scholars I am now putting this in front of. I will answer each as plainly as I can.
So what are you actually saying?
Interest secretly does two jobs inside one number. It charges for time, a fee for the mere passing of days, and that part is the riba. And it measures real risk, the chance the borrower defaults or the price moves. A 2025 theorem by Ackerer, Hugonnier and Jermann, in the journal Mathematical Finance, lets you cleanly separate those two jobs and switch off the time-charge, keeping only the risk measure. I call that measure kappa.
So you can price the things finance needs to price, credit, insurance, bonds, with no interest rate anywhere, not by wrapping interest inside a compliant-looking legal structure the way the industry does, but by removing it from the mathematics itself.
In one line: we removed interest from the pricing engine, not just from the paperwork. Because the riba was never really in the contract. It was in the rate used to price the contract.
How is kappa different from an interest rate?
This is the question that matters most, so let me be precise.
An interest rate, r, is rent on time. It is fixed in advance, guaranteed, flows in one direction (the borrower always pays the lender), and is owed even if nothing happens in the world. A perfectly safe bond still pays it.
Kappa is the tempo of a real event, a default, a loss, a price converging. It is measured from the market, not fixed in a contract. It moves. And when no real event can happen, kappa is simply zero, and you earn nothing.
So the whole difference fits in one sentence:
Interest pays you for time even when nothing happens. Kappa pays nothing when nothing happens.
That is not a play on words. It is the line between the two, and it is the line Islamic law draws around riba.
With kappa, do you sometimes pay and sometimes get paid? Like perpetual funding?
Yes, and that two-sidedness is one of the clearest signs it is not interest. It is exactly what I first saw on dYdX.
Say you are long a gold perpetual. This funding period it trades a tenth of a percent above the real price, so you, the long, pay that to the shorts. Next period it trades below the real price, so the shorts pay you. If it sits exactly at fair value, nobody pays anybody. You sometimes pay, sometimes receive, sometimes neither. It is an exchange between two equals in a market, pulling the contract back toward reality. There is no lender, no borrower, no guaranteed accrual.
Now compare a loan. You borrow a hundred at five percent, and you pay five a year, every year, in one direction, guaranteed, no matter what happens. That is riba: predetermined, owed regardless of outcome, charged for time alone. Perpetual funding is none of those things.
One precision, so I do not mislead you. Kappa is not the payment itself. Kappa is the speed, the rate at which that gap closes, which you read off how the funding behaves over time. The thing that changes hands is the premium; kappa is the measured rate behind it. And when kappa is used to price other instruments, the cashflows stay contingent: in mutual insurance you contribute to a shared pool and are paid only if a loss hits you; in a credit instrument the writer pays out only if a default actually happens. In every case money moves because a real event did or did not occur, never as a fixed reward for time passing.
Isn’t kappa just interest with a new name?
If it were, this would be a clever evasion worth nothing, so I hold it to a test that can fail.
There is a classical, threefold definition of riba, associated with the economist Mahmoud El-Gamal: the charge must be predetermined, independent of outcome, and levied for time alone. Kappa fails all three. It is not predetermined, it is measured after the fact. It is not independent of outcome, it is the outcome. And it is not charged for time, it is charged for an event.
And here is the test I would put to any skeptic. If kappa were secretly the interest rate, you could only ever recover it from interest-rate markets. But we recover the same kappa three independent ways that share no inputs: from credit spreads, from the convergence of perpetual prices, and, the one I find most convincing, from insurance loss records, the frequency with which crop failures and claims actually occur. There is no bond market in a register of failed harvests. There is no interest rate anywhere in it. Yet the same kind of number comes out, and on real sovereign bonds it lines up cleanly with credit rating, low for the safest issuers and rising for the riskiest, exactly as a measure of default risk should and exactly as an interest rate would not.
A quantity you can read off a record of failed harvests cannot owe its existence to LIBOR.
Then why couldn’t anyone just set interest to zero before?
Because in ordinary finance, setting the interest rate to zero breaks everything.
The interest rate is usually the only thing keeping a long-lived price finite. A bond that pays a coupon forever is worth the coupon divided by the rate; let the rate fall to zero and its value runs off to infinity. So "interest-free pricing" looked like a dead end in both directions: either broken, because you remove the rate and nothing can be priced, or empty, because you quietly slip the rate back in through a benchmark. For fifty years the industry, in practice, chose the second.
What that theorem showed, and what dYdX had stumbled into by engineering instinct, is a third way nobody had a tool for. When there is no interest, the price is no longer a stream discounted over infinite time. It is the expected value of the thing at a random future moment, the moment the contract converges or the event occurs. The horizon is held finite not by a discount, but by the event itself. As long as that event has some rate of happening, the price is finite and sensible, with no interest anywhere. The discount rate was never the only thing that could tame infinity. A real event can do it too, and a real event is not riba.
That paper is one year old. That is the honest answer to "why now." The tool did not exist. The formula was running on dYdX before the proof that it was sound, and before anyone saw that it generalizes.
Does this go beyond perpetuals?
That is the part that kept me up at night, and it is why this became seventeen papers instead of one trade.
If kappa can price a perpetual, the same mathematics prices the things finance actually runs on. A credit instrument whose fair price depends only on the chance of default and the recovery if it happens, with no interest in it. An insurance contribution equal to the honest expected loss, no more. A full term structure, the interest-free counterpart of the yield curve that every financial system is built on. Each paper carries the single idea into one more corner, and each is disciplined against real market data rather than left as theory.
And it became something running. There is a live prototype, a testnet where kappa is computed openly and continuously from market activity, and the early shape of an infrastructure layer where no interest rate appears anywhere: not in how contracts are priced, not in how the network rewards the machines that run it, not in any instrument on top. The absence of interest is not a rule bolted on afterward. It is the native grammar of the pricing, present in every block.
What are you not claiming?
This is where sincerity is tested, so I want to be exact.
This addresses riba, and only riba, and only at the level of pricing. It does not, by itself, settle the other questions Islamic law asks of a contract: gharar, excessive uncertainty; maysir, gambling; qabd, real possession of the thing traded. Those are separate pillars, and they belong to qualified scholars, not to a formula. The purely cash-settled contracts are the hardest case of all, and I treat them as the hardest, not the easiest. I make no claim that any of this is "compliant," and I have issued no fatwa and never will. As I write this, the argument is in front of qualified Shariah scholars, and what I have asked them for is not a blessing but the opposite: to find where it is wrong.
It is also not a free lunch. Removing the rent on time has real costs. Risk-sharing extends credit more cautiously than collateralized lending does. How this behaves over very long horizons is a genuinely open question I cannot yet answer. And because the central number becomes a measurement rather than a committee's decision, the integrity of that measurement becomes the thing an adversary would attack. I would rather name these weaknesses myself than have them found, because a foundation that hides its soft spots is not a foundation.
What are you asking of scholars who read this?
Three things, in order.
First, an honest judgment on one narrow question: does setting the interest term to zero remove riba in substance, and is kappa genuinely a measure of real risk rather than interest under another name? Yes, no, or yes-with-conditions.
Second, if you cannot conclude yet, tell me exactly what you would need to see to decide.
Third, if you find the idea sound, a proper, scoped review, beginning with the asset-backed instruments where a real underlying exists, and leaving the hardest cash-settled case for last.
What I am not asking for is a stamp. I have only argued that this is not interest in disguise. That is the first gate, not the last, and the rest is genuinely your judgment. I would rather build the review slowly and correctly than rush a conclusion.
Where this leaves us
For fifty years, "interest-free pricing" looked like one of two things: trivial and broken, or impossible and dishonest. What I am proposing is that it is neither. It is a consistent way to price what finance needs to price, built on a measured, non-zero substitute for the interest rate, that contains no charge for time. The thing interest did, putting a coherent price on time and risk, turns out to be doable by the tempo of a real event, which has no interest in it at all.
If that survives the scrutiny it is now under, and scrutiny is exactly what I am asking for, then this is not a patch on Islamic finance. It is a different foundation underneath it.
It started with an interest rate that wasn't there. I am still amazed it was that simple to see, and that hard to believe.
If you work on these questions, as a scholar, an economist, or a builder, I would genuinely value your scrutiny, especially the kind that tries to break the argument. The seventeen working papers are open for examination on my SSRN author page: https://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=10250376, and the live prototype, where kappa is computed in the open from real market activity, is at kappachain.site. The most useful thing you can do is try to prove me wrong.
Shehzad Ahmed is the founder of Arcus Quant Fund and Baraka Protocol.