In decentralized finance (DeFi), stablecoins like DAI are designed to offer a stable value amidst the fluctuating nature of cryptocurrencies. We examine the class of crypto-backed stable derivatives, with a focus on mechanisms for price stabilization, which is exemplified by the well-known stablecoin DAI from MakerDAO. For simplicity, we focus on a single-collateral setting. We introduce a belief parameter to the simulation model of DAI in a previous work (DAISIM), reflecting market sentiments about the value and stability of DAI, and show that it better matches the expected behavior when this parameter is set to a sufficiently high value. We also propose a simple mathematical model of DAI price to explain its stability and dependency on ETH price. Finally, we analyze possible risk factors associated with these stable derivatives to provide valuable insights for stakeholders in the DeFi ecosystem.

翻译：在去中心化金融（DeFi）领域，DAI等稳定币旨在加密货币价格波动背景下维持价值稳定。本文研究加密资产支持的稳定衍生品类，重点分析以MakerDAO知名稳定币DAI为代表的价格稳定机制。为简化分析，我们聚焦于单抵押品场景。在前期工作DAISIM模拟模型基础上引入信念参数，用以反映市场对DAI价值与稳定性的看法，结果表明当该参数设定为足够高的数值时，模型能更准确地匹配预期行为。我们同时提出DAI价格的简易数学模型，解释其稳定性机制及与ETH价格的相关性。最后，分析此类稳定衍生品相关的潜在风险因素，为DeFi生态系统的利益相关方提供重要参考。