Price stability has often been cited as a key reason that cryptocurrencies have not gained widespread adoption as a medium of exchange and continue to prove incapable of powering the economy of decentralized applications (DApps) efficiently. Exeum proposes a novel method to provide price stable digital tokens whose values are pegged to real world assets, serving as a bridge between the real world and the decentralized economy. Pegged tokens issued by Exeum - for example, USDE refers to a stable token issued by the system whose value is pegged to USD - are backed by virtual assets in a virtual asset exchange where users can deposit the base token of the system and take long or short positions. Guaranteeing the stability of the pegged tokens boils down to the problem of maintaining the peg of the virtual assets to real world assets, and the main mechanism used by Exeum is controlling the swap rate of assets. If the swap rate is fully controlled by the system, arbitrageurs can be incentivized enough to restore a broken peg; Exeum distributes statistical arbitrage trading software to decentralize this type of market making activity. The last major component of the system is a central bank equivalent that determines the long term interest rate of the base token, pays interest on the deposit by inflating the supply if necessary, and removes the need for stability fees on pegged tokens, improving their usability. To the best of our knowledge, Exeum is the first to propose a truly decentralized method for developing a stablecoin that enables 1:1 value conversion between the base token and pegged assets, completely removing the mismatch between supply and demand. In this paper, we will also discuss its applications, such as improving staking based DApp token models, price stable gas fees, pegging to an index of DApp tokens, and performing cross-chain asset transfer of legacy crypto assets.