The paper develops a new monetarist DSGE model to examine the macroeconomic implications of fiat-money-backed stablecoins and the effectiveness of prudential policies in mitigating associated risks. The model features two segmented sectors: a centralized real economy where fiat money facilitates consumption and investment, and a decentralized virtual economy characterized by anonymous bilateral search and matching, in which transactions are exclusively conducted using stablecoins. Calibrated to the U.S. economy, the simulation results reveal that stablecoins amplify the propagation of exogenous shocks to key macroeconomic variables by weakening the effectiveness of monetary policy. However, prudential regulations—specifically those governing the backing ratio of stablecoins to fiat-denominated reserve assets, analogous to banking liquidity requirements—can serve as stabilizing instruments, dampening volatility and enhancing macroeconomic resilience in the presence of stablecoins.