LMSR

How it works

A constant-product provider's exposure has no upper bound. As the price moves, the position converges on holding only the losing side, and the loss against simply having held the two tokens grows without limit. Everyone knows this and nobody can quote it, because the answer depends on where the price goes and the curve quotes at every price there is.

Robin Hanson's logarithmic market scoring rule was built for exactly this problem, in prediction markets, in 2003: a market maker that will always quote, and whose total loss is bounded by a constant chosen when the market opens. The bound is the whole reason it is used. It has never been the curve of a general-purpose AMM because a bounded-loss maker must also be a bounded-*range* maker, and a pool that stops quoting past a price is a worse product right up until the day it is the only pool that did not get emptied.

This pool holds the invariant exp(-reserve0 / b) + exp(-reserve1 / b) = k which prices token0 in token1 at exp((reserve1 - reserve0) / b): exactly one at balance, falling smoothly as the pool fills with token0. The parameter `b` is depth and it is also the bound. Larger `b` is flatter near parity and a wider quoting range; smaller `b` is a tighter market that gives up sooner.

There is one number to choose and it means one thing. What a provider gets that no constant-product pool offers is a figure: {maxLoss} is what this curve can cost them in the worst case anybody can construct, published on-chain, before they deposit. Beyond the range the curve refuses the trade instead of quoting a price it cannot honour, which is the same promise stated from the other end.

Using it

Uniswap v4 removed hookData from initialize, so per-pool parameters arrive out of band. Fix them for a pool key whose pool does not exist yet, then initialize. Nobody can change them afterwards, including you.

poolManager.initialize(key, startingSqrtPriceX96);

Parameters

This hook takes no per-pool configuration.

From TypeScript

npm i @hookforge/sdk

import {getHook, hookAddress, poolKeyFor} from "@hookforge/sdk";

const hook = getHook("lmsr");
const key  = poolKeyFor({
  hook: hookAddress("lmsr", 8453),   // Base
  currencyA: USDC, currencyB: WETH,
  tickSpacing: 60,
});

What it reverts with

The callbacks it claims

Uniswap v4 reads a hook's permissions from the low fourteen bits of its own address, which is why deploying one means mining a CREATE2 salt. This hook claims 5, so every deployment of it has an address ending in 0x2a88.

• beforeInitialize
• afterInitialize
• beforeAddLiquidity
• afterAddLiquidity
• beforeRemoveLiquidity
• afterRemoveLiquidity
• beforeSwap
• afterSwap
• beforeDonate
• afterDonate
• beforeSwapReturnsDelta
• afterSwapReturnsDelta
• afterAddLiquidityReturnsDelta
• afterRemoveLiquidityReturnsDelta

It says what it is, on-chain

Nothing about a hook's address tells an indexer, a wallet, a router or an agent what the pool does, which is why hook discovery today is a curated list. This hook answers for itself, in one eth_call, with no registry in the loop.

cast call $HOOK "hookName()(string)"    # LMSR
cast call $HOOK "specURI()(string)"     # https://lmsr.pages.dev/hook.json
cast call $HOOK "hookTags()(string[])"  # curve, custom-curve, bounded-loss, scoring-rule, no-admin

Build, test and deploy

git clone --recurse-submodules https://github.com/nirholas/lmsr
cd lmsr
forge build && forge test

# Dry run: mines the salt, prints the address, sends nothing.
forge script script/Deploy.s.sol --rpc-url $RPC_URL

# For real.
forge script script/Deploy.s.sol --rpc-url $RPC_URL --broadcast --verify

Try it

This is the hook running, not a picture of it. Connect a wallet on a chain it is deployed to, or bring the whole stack up locally in one command and use it with no funds and no wallet risk at all.

git clone --recurse-submodules https://github.com/nirholas/lmsr
cd lmsr

anvil &
forge script script/DeployLocal.s.sol --rpc-url http://127.0.0.1:8545 --broadcast \
  --private-key 0xac0974bec39a17e36ba4a6b4d238ff944bacb478cbed5efcae784d7bf4f2ff80

node web/build.mjs && npx serve web/dist