  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.
