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What Is the Role of a Stability Mechanism like an Automated Market Maker (AMM) during a De-Peg Event?

An AMM, such as a liquidity pool on a decentralized exchange (DEX), is a crucial stability mechanism. It provides a source of liquidity for traders to swap the de-pegged stablecoin for a pegged asset.

The AMM's bonding curve is designed to incentivize arbitrage by making the de-pegged asset cheaper. However, during a death spiral, the pool's liquidity can be quickly drained by panic sellers, leading to high slippage and rendering the AMM ineffective at restoring the peg.

How Does a Constant Sum Market Maker ($x+y=k$) Differ from a Constant Product AMM?
What Role Did the “Anchor Protocol” Savings Rate Play in the Initial Confidence and Eventual Panic Surrounding Terra/Luna?
How Do AMMs with Dynamic Fees Adjust to Mitigate the Impact of Arbitrage on Liquidity Providers?
What Are the Advantages and Disadvantages of Using a Constant Sum Formula versus a Constant Product Formula in an AMM?