Virtual Price

Definition

Virtual price is defined as

virtualPrice = totalAssetBalance / totalLpSupply

where totalAssetBalance is the summation of all balances of underlying assets and totalLpSupply is the total supply of LP tokens.

Example A (Virtual Price Calculation): Suppose the pool has two stablecoins USDT/USDC with balances [1M, 1M] and the total supply of syUSD (LP token) is 1.5M, then the virtual price is (1M + 1M) / 1.5M = 1.3333.

Virtual Price as Exchange Rate

For any pool operations that converts LP token from/to underlying asset (e.g., mint syUSD with USDT or redeem syUSD for USDC), virtual price is essential the exchange rate between the LP token and underlying asset if no penalty (e.g., slippage cost) happens.

Example B (Redeem without Penalty): Suppose the pool has two stablecoins USDT/USDC with balances [1M, 1M], total supply of syUSD (LP token) is 1.5M, and soft weights are [0.6, 0.6]. Redeeming 0.1M syUSD for USDC will not incur a penalty (as the resulting percentages are [0.5263, 0.47368]), and as a result, the pool will return 0.13333M USDC for the redemption (virtual_price = 1.3333).

Example C (Redeem with Penalty): Suppose the pool has two stablecoins USDT/USDC with balances [1M, 1M], total supply of syUSD (LP token) is 1.5M, and soft weights are [0.6, 0.6]. Redeeming 0.5M syUSD for USDC will incur a penalty (as the resulting percentages will exceed 0.6), and as a result, the pool will return less than 0.6667M USDC for the redemption (virtual_price = 1.3333).

One common mistake in calculating virtual price is to use the exchange rate of a transaction as virtual price, which is incorrect if such a transaction incurs a penalty.

Virtual Price Property

One key property of virtual price is that the value should be non-decreasing to reflect the accumulated interest + swap fee + penalty fee, i.e., the value of per LP token is self-value-accrued over time by earning interest + swap fee + penalty fee automatically.

Example D (Virtual Price with Fee): Suppose the pool has two stablecoins USDT/USDC with balances [1M, 1M], total supply of syUSD (LP token) is 1.5M. Suppose a user swaps 0.1M USDT for 0.09M USDC, the resulting pool becomes [1.1M, 0.91M], and thus the virtual price increases from 1.3333 to 1.34.

Example F (Virtual Price with Interest): Suppose the pool has two stablecoins USDT/USDC with balances [1M, 1M], total supply of syUSD (LP token) is 1.5M. After some time, the pool earns interests [0.1M, 0.15M] respectively. As a result, the virtual price increases from 1.3333 to 1.5.

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