General Automated Market Maker

Omnipair is powered by a Generalized Automated Market Maker (GAMM), a primitive that combines constant-product AMM functionality with isolated lending logic. This allows a single pool to support both spot trading and margin borrowing without oracles or centralized risk config.

Each pool holds a token pair and provides:

• Swap functionality via spot prices

• Margin borrowing based on time-weighted EMA prices

• Interest accrual via utilization-based dynamic rates

• Liquidation through write-offs and streaming collateral

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Each pool is defined by two tokens ($x$, $y$). Liquidity is added in a constant product — $(xy = k)$ where $k = L^2$ — fashion, and reserves are tracked.` Each pool contains two types of reserves:

• Virtual Reserve

• Actual Reserve

1. Spot Price

Derived from the pool's token virtual reserves:

$$\text{Spot Price }_{0 \rightarrow 1} = \frac{\text{Virtual Reserve}_1}{\text{Virtual Reserve}_0}$$

Used for swap execution and is updated by every spot trade, while Lent liquidity is not calculated in the virtual reserves:

$$\text{Reserve}_{actual} = \text{Reserve}_{virtual} - \text{Reserve}_{debt}$$

2. Time-weighted EMA Price (Lending price)

A time-weighted Exponential Moving Average of the spot price. EMA pricing smooths volatility and prevents manipulation around liquidation events.

$$\text{EMA}(t) = \alpha \cdot \text{Price}(t) + (1 - \alpha) \cdot \text{EMA}(t - 1)$$

Where:

$$\alpha = 1 - e^{-\frac{\Delta t}{\tau}}$$

• : Time since last update

• $(\tau)$: Exponential decay constant (half-life converted to continuous time)

This price is used to compute borrowing power and liquidation thresholds.