Time-Dynamic AMM

Exponent yield assets have maturities, inherently impacting their price in a way that traditional AMMs are not designed to accommodate, as they typically don’t handle assets that expire or depreciate at maturity.

To enhance capital efficiency in trading Exponent yield markets and better manage impermanent loss, Exponent has developed a novel Time-Dynamic AMM specifically tailored for Solana assets with maturities. This AMM considers price ranges for maturing assets and dynamically concentrates the trading curve to optimize price execution.

The AMM also includes a Flash Swap mechanism, inspired by Pendle’s design, allowing liquidity providers to supply liquidity for both volatile (yield shares) and fixed yield markets (Income Tokens) with a single asset price exposure. All volatile and fixed yield trades occur within a single market, resulting in increased trading volume and higher swap fees for liquidity providers.

For capital efficiency and because Exponent’s AMM dynamically concentrates the liquidity as Income Tokens approach maturities, each AMM pool features Income Tokens paired with their underlying asset. With AMMs that use predefined formulas to allocate capital across a continuous spectrum of prices, pairing assets with others that are correlated by price is more efficient. When the paired assets’ prices are strongly correlated, the price curve can be tighter, significantly reducing price divergence and, consequently, impermanent loss. To maximize returns for liquidity providers and enable a shared liquidity pool with volatile yield/yield share trades (through flash swaps), the underlying asset is in the form of a Liquid Yield Token (LYT), which represents the tokenized position of the yield market.

For example, an Income Token based on ‘marginfi SOL’ would be paired with marginfiSOL (SOL lent on marginfi). This pairing is further justified by the fact that yield from lent SOL is paid in SOL, making the yield component for Exponent’s Income Token naturally expressed in SOL.

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Time-Dynamic Sensitivity

A unique aspect of Exponent’s AMM is its time sensitivity, which factors the time-dependencies of Exponent yield markets as they have maturities/expiries that could impact the capital value of liquidity providers’ funds as well as cause inefficient price impact for traders.

As Income Tokens and yield shares near maturity, market volatility contracts. At maturity, a yield share has no remaining yield to distribute, making its price essentially zero, while an Income Token—representing a claim on the principal—also stabilizes at a fixed redemption value. The further from maturity, the greater the risk and volatility tied to these duration assets.

As such, the AMM gradually reduces trade sensitivity over time based on the maturity of the assets as well as yield accrued. Early in the maturity period, the curve is highly sensitive to trades since significant yield available. By maturity, however, trades have zero price impact since no further yield is distributed. By dynamically concentrating liquidity within a narrow range based on maturity, the AMM can capture higher trading volumes for liquidity providers and offer more optimal trade execution for traders.

In addition to time sensitivity, Exponent’s AMM also considers time decay — the progressive decrease in value of yield shares as they approach maturity and eventually reach zero. As a result, the AMM has no active liquidity for volatile yield shares, while still allowing both volatile and fixed yield markets to operate through a single liquidity pool. This is made possible by using a novel AMM mechanism called Flash Swap.

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Flash Swap

In an Exponent liquidity pool, Income Tokens are paired with the underlying asset (such as USDC) deposited in the underlying protocol. This design allows swaps between Income Tokens and the underlying asset directly, not between Income Tokens and yield shares. Since Income Tokens and yield shares are derived from the same tokenized position/LYT, their prices are inherently correlated. Exponent leverages this relationship by using a single liquidity pool to support trading for both Income Tokens and yield shares belonging to the same market. This single-pool design not only enables liquidity providers to earn from both fixed and volatile yield trading but also simplifies liquidity management.

Put simply, Income Tokens and yield shares combined are worth 1 unit of the original deposit stripped through Exponent Prism. Therefore, when a user buys Income Tokens, it inversely affects the price of yield shares, and vice versa. Exponent’s AMM uses this correlation to temporarily lend (flash lend) liquidity to the trader, making it more efficient for both liquidity providers, as they don’t need to deal with managing time decay for yield shares, and for traders, who can tap into the liquidity of Income Tokens instead of having two separate pools for volatile and fixed yields. When a trader buys or sells yield shares, the AMM borrows against the liquidity in the pool for the trade, and this “flash loan” briefly impacts the liquidity pool and the price of the yield markets:

• Buying yield shares: When a user buys yield shares, the AMM deposits the user’s funds into the underlying protocol to mint yield shares. During this process, Income Tokens are also minted and immediately sold for the underlying asset in the pool, repaying the liquidity used. This transaction impacts the price of Income Tokens as a result of the yield shares purchase.
• Selling yield shares: When a user sells yield shares, the AMM borrows an equivalent amount of Income Tokens from the pool. It then combines the yield shares with the borrowed Income Tokens to redeem the underlying asset (LYT) from the protocol. Part of the redeemed LYT is sold back in the pool to repay the borrowed Income Tokens, affecting the price of Income Tokens as a result of the yield shares sale.

In summary, although only Income Tokens and LYTs are held in the pool, this mechanism enables Exponent’s AMM to efficiently manage trades for both fixed and volatile yield markets through a single liquidity pool, using flash swaps to provide instant liquidity for yield share trades.