Decentralized Governance of Stablecoins with Closed Form Valuation

We model incentive security in non-custodial stablecoins and derive conditions for participation in a stablecoin system across risk absorbers (vaults/CDPs) and holders of governance tokens. We apply option pricing theory to derive closed form solutions to the stakeholders' problems, and to value their positions within the capital structure of the stablecoin. We derive the optimal interest rate that is incentive compatible, as well as conditions for the existence of equilibria without governance attacks, and discuss implications for designing secure protocols.