HOT: an automated market maker repriced by signed quotes

An automated market maker (AMM) quotes from its own reserves. When the price moves on a centralised exchange, the AMM’s quote stays where it was until someone trades against it. The first trader to notice buys the underpriced asset from the pool and sells it elsewhere, and the pool’s liquidity providers pay for that trade. The cost is measured as loss-versus-rebalancing (LVR), a term from Milionis and co-authors.

The usual defence is a higher trading fee, which also taxes the ordinary traders the pool wants. Hybrid Order Type (HOT), designed under contract for Arrakis Finance in 2024, takes another route. It gets a current price into the pool often and cheaply, and charges for staleness only while the price is stale.

Two ways to trade against one pool

The first is a signed quote. A solver, a firm that competes to fill users’ orders in intent-based trading systems, asks the pool’s quoting service for a price. The service returns a quote signed under EIP-712: a maximum amount, a price, an expiry, the one address allowed to submit it and the one allowed to receive the proceeds. The solver submits the quote with its trade. The price is fixed for the life of the quote, and the quote can be partly filled.

The second is an ordinary swap, open to anyone, against a concentrated-liquidity position that behaves like a single Uniswap v3 range.

Both draw on the same reserves, with one distinction. Signed quotes can trade at any price inside configured bounds, so the pool’s holdings can end up in any proportion. The balanced part of the reserves, which fits the range position, is available to both kinds of trade. Anything beyond it can be reached only by signed quotes.

The quote carries the pool’s next price

Besides the solver’s own terms, each quote contains a new spot price for the open pool and new fee settings. When the quote is validated on-chain, the pool adopts them. The solver pays the gas, and the pool’s price is brought up to date as a by-product of a trade that was happening anyway.

The quote names two prices for the solver. The better one goes to the first solver in a block whose quote updates the pool. The other applies to quotes that are valid but arrive after the update. Solvers therefore compete to be the one that delivers the fresh price.

A fee that grows with the age of the price

For open swaps, the fee on each input token is

fee = minimum + growth rate × seconds since the last quote was signed

up to a maximum. All three settings arrive with the quotes. The growth rate is set to the expected change in the market price per second, so it rises with volatility.

Take a minimum of 1 bp and a growth rate of 0.5 bp per second, figures chosen for illustration. Just after an update a swap pays 1 bp. Twelve seconds later, one Ethereum block, it pays 7 bps. An arbitrageur profits only if the market has moved by more than the fee, and the fee has been rising at the speed the market is expected to move. If quotes land every block, the fee stays near its minimum, and ordinary traders pay less than they would to a pool whose flat fee has to cover stale prices all the time.

The clock starts when the quote was signed. A quote that reaches the chain late updates the pool to a price that is already a few seconds old, and the fee counts those seconds.

What the contract checks

The quoting service is trusted to sign sensible prices. The contract limits the damage if it fails to.

• A quoted price must be within a set deviation of an on-chain reference oracle.
• Each quote has a maximum amount, an expiry, and a nonce that prevents replay.
• The number of quotes accepted in one block is capped.
• The minimum fee has a floor in the contract that the quoting service cannot go below. It stands for the smallest error assumed in any signed price.

If the quoting service stops, the open pool continues to trade. Its fee climbs to the maximum and stays there until quotes resume.

What is established, and what is not

The whitepaper specifies the mechanism and argues that fresher prices and a time-based fee reduce what arbitrageurs can take. It contains no backtest. Arrakis’s launch post put the reduction in LVR exposure at 50 to 90 percent, and presented the figure as its own estimate. The size of the benefit depends on how often quotes land, which depends on solver demand for the pair, and on whether the growth rate keeps pace with real volatility. Both have to be measured pool by pool.

HOT is built as a module on a modular pool, which supplied custody, permission checks and the oracle hook. The note on modular pools describes that split.