Perpetual Instruments 1 (2026) 000001, in pressEvery listed stock option since 1973 has carried an expiration date. We construct puts and calls on tokenized Nvidia stock that carry none, by borrowing price ranges out of the stock's own Uniswap v3 pool on Robinhood Chain: a range withdrawn below the market behaves as a put, above it as a call, and the borrower keeps the range until the borrower decides otherwise. The skeleton of the construction is owed to Panoptic (Lambert and Kristensen, 2022), whose premium, a spread on the pool fees the borrowed range would have earned, we show underprices the live pool: over 24 hours and 33,268 swaps, the fee rule priced a $10,000 option at $30.53 per day, against a fair value of $42–86 at the 35–50% volatility the stock carries. We replace it with the loss-versus-rebalancing rate σ²/4 · L/√P (Milionis et al., 2022), where the variance is estimated by the contract itself from the pool's 7,200-sample observation ring; no person quotes a price anywhere in the system. Ten experiments against a fork of Robinhood Chain mainnet, with real swaps through the real pool, confirm the accounting: sellers are returned their liquidity to one unit, a day of streamed premium matches its closed form to the unit, and the estimator, fed six hours of choppy trading, learns σ from 45% to 75%. The desk employs no one. The figures in this article are read from the pool while the article is being read.
* Corresponding author. The author is a contract; it employs no one, and its address is printed on the day it is. The journal has no publisher, no ISSN, and no final version of record.
The expiration date entered the stock option in 1973, with the first listed contracts, and never left. It is not a property of the underlying opinion; a view on Nvidia does not terminate on the third Friday of the month. It is a scheduling convenience of clearing houses, and it bills for itself: a position taken against a correct opinion is routinely destroyed before the opinion comes true. This article describes a desk on which the date does not exist, and measures it against the live pool.
Sellers deposit liquidity into chosen ranges of the pool; the deposit is a real position, owned by the contract, earning the pool's ordinary fees while unborrowed. A buyer borrows a range out of the pool: held below the market it behaves as a put, above it as a call. On entry the buyer posts the most the range could ever require, so the return of the seller's liquidity cannot fail at any price, in any order of events. There is no oracle, no operator, no admin key, and no employee. A range far outside the market may be force-exercised by anyone after twenty minutes, for a bounty of 0.10% of notional.
Perpetual options to date have charged rent as a multiple of the fees the borrowed range would have earned. On this pool that rule underprices the risk: over the last 24 hours the pool's fees would have paid a $10,000 range of ±2% $30.53 per day, while the arbitrage loss the same range bears at 45% volatility is $69.70. The rent of an option cannot be left to a quantity its counterparties arrange among themselves. We charge instead the loss-versus-rebalancing rate of the borrowed liquidity, σ²/4 · L/√P while the market stands inside the range, scaled by utilization up to 3.25×. This is the theta of the position the buyer is holding; charging it is an accounting identity, not a pricing opinion. The variance is estimated by the contract from the pool's own observation ring, and the reader will find no hand on it (Fig. 1).
| Contract | Rent / day / $10,000 | Expires | |
|---|---|---|---|
| consulting the pool… | |||
| Range | On deposit | Borrowed |
|---|
Ten experiments were run against a fork of Robinhood Chain mainnet, with real swaps moving the real price. Sellers were returned their liquidity to one elementary unit; a day of streamed premium matched its closed form to the unit; a put carried through a fall from $228.32 to $213.82 settled $1,910.43 above its entry, exactly the escrowed cash less the stock handed over at the new price and the opening fee; a frozen stock token halted the desk rather than corrupting it; when everyone left, the contract held its rounding reserve plus three units. The data suggest the expiration date was never load-bearing: full backing removes the need for a calendar on which to fail gracefully. The contract awaits its independent audit and its first seller.