Technical Overview

Logarithm Finance introduces a market-neutral market-making platform engineered to enhance and consolidate on-chain liquidity while simultaneously distributing the risk borne by liquidity providers (LPs). The core components of Logarithm encompass automated delta-neutral vaults, which streamline the experience for LPs, and a hedging module specifically optimized to mitigate the market risk associated with long-tail assets. As a product, Logarithm enables the partitioning of market risk related to liquidity provision and impermanent loss, thereby fostering novel opportunities ranging from genuine yield generation in blue-chip market making to cost-effective and dependable yield farming.

Logarithm Finance's first product is the Nautilus Vault. It connects the Uniswap V3 pool with the GMX decentralized exchange, allowing for balanced liquidity provision. This means that any risk from Uniswap V3 is offset by a short position on GMX. Users can deposit assets into the Nautilus Vault. The Nautilus Vault automatically finds the best way to split the capital between the liquidity provision and the hedge position. The liquidity part is converted into the right amounts of the token pair for the chosen Uniswap V3 pool and creates a concentrated liquidity position. The hedge part is used to open a leveraged short position on GMX, which removes the price risk of the liquidity position. As a result, users get a balanced, concentrated liquidity position that generates a predictable return on their assets.

The vault actively keeps track of the assets in the concentrated liquidity position and any hedge deviations. When the hedge deviation exceeds a certain limit, the vault's composition is adjusted to regain balance. The vault also monitors the current spot price for the selected pool and modifies its base liquidity range if the spot price goes outside a set range.

Base range, trigger range, and rehedge thresholds are decided based on backtests and influenced by market volatility. During low volatility periods, maintaining narrow ranges is more profitable, as it increases revenue from Uniswap fees. In times of high volatility, the vault automatically expands liquidity ranges and decreases the rehedge threshold, making the strategy more conservative.

Due to the nature of Uniswap V3's concentrated liquidity, it can be challenging to work with exact token amounts, and small leftover tokens, or "dust tokens," can appear during rebalancing. To address this and improve capital efficiency, the vault automatically creates an additional limit range at the spot price of the DEX pool. The other boundary is set at either the bottom or top range of the base position, depending on the dust composition of the pool. The limit range is adjusted during each liquidity operation of the Uniswap V3 Vault.

Besides monitoring the internal hedge state, the vault also tracks the historical fees generated by the DEX pool and GMX borrowing rate. If market conditions become unfavorable for the vault (meaning the revenue from fees doesn't cover the borrowing rate costs), the vault can automatically decide to exit the position and convert its capital back to the notional asset. This feature ensures that the vault remains efficient and profitable under various market conditions.

In the initial iteration of the Nautilus Vault, the Logarithm team will set and manage most of the critical vault parameters based on internal backtests. This approach ensures flexibility and responsiveness during the early stages of operation and aligns with the practices of other active liquidity managers at the time. However, this is not the ultimate state, as Logarithm aims to push the boundaries of permissionless and autonomous DeFi protocols. To achieve this, the Logarithm team will introduce a special service contract called Logarithm Beacon.

Logarithm Beacon is a permissionless modular contract that can gather and store historical data from other contracts, making it available for the Nautilus Vault execution module. This contract will trustlessly store data such as historical prices, volatility, funding rates, pool fees, and more. The Nautilus Vault will access this data and automatically adjust its internal state based on current market conditions. This will transform Nautilus Vaults into a fully autonomous financial entity that can function without human intervention. The utilization of Logarithm Beacon will extend beyond Nautilus Vault, enabling the development of a suite of sophisticated autonomous financial products under the Logarithm Finance umbrella.

It is essential to recognize that such innovation has only become possible due to roll-up scaling technologies introduced by L2 solutions like Arbitrum. Storing vast amounts of historical data and executing complex tasks based on it was not feasible on L1 Ethereum because of high gas costs. Many DeFi protocols on Ethereum had to compromise their trustless nature by relying on off-chain computations and permissioned keepers. With few exceptions, DeFi protocols currently deployed on L2s are repeating the same mistakes, despite solutions like Arbitrum offering a more robust and capable execution environment. By introducing Logarithm Beacon, Logarithm Finance aims to push the boundaries of Autonomous DeFi on Arbitrum.

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