# Parallelizer Module ## Introduction The Parallelizer Module is one of the main minting modules of Parallel stablecoins. It is conceived as a basket of different assets which can all be used to mint or burn the stablecoin at oracle value. It comes with automated mechanisms to maintain the exposure to each asset in the reserves within reasonable bounds. This enables the system to properly segregate and diversify the risks between the assets in its backing, and guarantees at the same time that in case of a black swan event the system does not end up over-exposed to the weakest assets of its reserves. The Parallelizer Module supports three main user actions: Mint, Burn and Redeem. The mint and burn actions rely on the idea that each asset in the reserves has a target price used to assess whether the asset is depegging and some conservative measure must be taken or not. Practically speaking, the three operations work as follows: * **Mint:** Stablecoins can be minted at oracle value from any of the supported assets with adaptive fees provided that the deviation of the asset used with respect to its target price is reasonable. * **Burn:** Stablecoins can be burnt at oracle value for any of the assets in the backing with adaptive fees, provided that the deviation of all assets respective to their target price are reasonable. The idea is to avoid capital outflows changing the exposures of the system in times of uncertainty. * **Redeem:** Stablecoins can be redeemed at any time against a proportional amount of each asset in the backing. Users should have a way to exit at any time, and so this feature is available in any conditions.

Built as an improvement of classic price stability modules (e.g. Sky) for stablecoin protocols, the Parallelizer system is designed with the following key properties: * **Scalability:** The Parallelizer enables minting and burning with limited fees from a wide range of assets. Its mechanisms work similarly with $1m TVL as with $1bn TVL. * **Resilience:** The underlying mechanisms of the Parallelizer system are all fully autonomous and predictable by all types of stakeholders. In case of a black swan event, the Parallelizer provides reasons to bet on the stablecoin returning to its target price. * **Trustlessness:** The Parallelizer is able to autonomously withstand unforeseen events, such as collateral depegs or hacks, without requiring any governance intervention. * **Fairness:** There cannot be any bank run as redemptions are thought to break sequentiality between users. * **Robustness:** The Parallelizer can be used as a basket of different stablecoins or assets allowing collateral risk to be well diversified. * **Safety:** If fees are properly set, the design provides incentives to bring the basket of reserves to a target desired allocation. In case of a depeg, it is unprofitable to perform trades that leave the protocol holding weak assets. * **Gas-efficiency:** Thanks to a range of different optimizations, the system is able to minimize the gas needed to interact with it. * **Modularity:** The system can not only accept any type of asset in the backing, its implementation is such that it can work for any type of stablecoin. On top of that, it is fully compatible with the other protocol’s minting modules: it works in parallel with the bridging module, savings module & flashloan module. ## Mint & Burn In the Parallelizer, it is possible to mint and burn the stablecoin for any of the asset in the collateral at a variable price. On top of the current oracle value of the asset, the price at which mints or burns happen also depend on whether the asset that is used is currently depegging or not. Practically, this is done by tracking for each asset in the backing a target price denominated in the stablecoin’s base currency. This target value for a collateral can be either absolute or updated relatively frequently. The stablecoin can be burnt for any asset in the backing. Contrarily to the mint case, the price at which the stablecoin is burnt does not only depend on the price of the asset for which it is burnt, it also depends on the price of all the other stablecoins in the backing. For all assets in the backing, the system looks into their deviation with respect to their target price and then applies to the burn price a penalty equal to the largest deviation possible. In its normal state, the stablecoin can be burnt for any of the assets in the system at their fair value which guarantees a small slippage for burning the asset. But in case of a depeg of one of the asset in the backing, this mechanism is meant to preserve the system’s exposures to all assets. As the stablecoin can be burnt for the same value of assets regardless of the asset it is burnt for, it disincentivizes stablecoin holders from rushing to exit towards the safest asset. The availability of these mint and burn functions allow any arbitrageur to take advantage of price deviations of the stablecoin on the secondary market to bring the stablecoin back to peg.

While the values at which mints and burns are taking place are one way for the Parallelizer system to control its relative exposures to the assets it has in reserves, the Parallelizer also relies on a variable fee mechanism to enable exposure to each asset to converge to a target area. Contrarily to the redemption case, a mint or a burn for one asset affects the system’s exposure to all its backing assets.

And so fees for a mint or burn operation depend on the exposure to the concerned asset after the operation, as a way to prevent the exposure from going beyond certain lower and upper limits. For instance, mint fees can be set to a high value (100%) when the exposure is above a target exposure, while burn fees can be made low to incentivize reducing the exposure. Conversely, when exposure to an asset is below the target window, mint fees can be set low and burn fees high to incentivize users to increase the system’s exposure to this asset.

With this, it is still possible that exposures go over the bounds where for instance mint fees reach 100%. The reason is that when you burn for an asset, you’re mathematically increasing the exposures to all other assets in the system. Assume the system is targeting a 40% maximum exposure for a stablecoin *USDb*, and so far 33 USDp have been issued with *USDa*, 33 with another stablecoin *USDc* and 33 with *USDyield*, then someone burning 15 USDp for *USDyield* would bring the exposure to *USDb* to above 40%. It should be at this point impossible to mint USDp with *USDb*, but burning USDp for *USDb* should come at a low cost. In the Parallelizer, there can be negative fees to incentivize people to come with a certain asset. The system however verifies that this does not open arbitrage loops. It is impossible to set negative mint fees if these are in absolute value bigger than the positive burn fees for all the other assets in the system. Below is an example of how a rebalancing operation may look like in the case of USDp:

## Redeem The redeem feature allows users to exchange their stablecoins for a proportional share of the underlying reserve assets at any time. This mechanism is designed to ensure fairness, especially during market stress scenarios, by preventing early redeemers from gaining an advantage over others. * **Proportional Distribution:** Upon redemption, users receive a mix of reserve assets proportional to their share of the total stablecoins, adjusted by a penalty factor. This ensures that no single user can deplete specific assets, maintaining system balance. * **Penalty Factor:** A dynamic penalty is applied during redemption, particularly when the system’s collateral ratio falls below 100%. This serves to: * **Deter Bank Runs:** Users receive less than the fair value if they attempt mass redemptions during downturns. * **Incentivize Stability:** Encourages users to hold their stablecoins, allowing the system time to recover. For example, if the collateral ratio drops to 98.5% due to a depeg, and the penalty factor is set to 0.98, a user redeeming 10 USDp might receive assets worth approximately $9.65 instead of $9.85, thereby contributing to the protocol’s re-collateralization. The figures below show the effect of burning with respect to redeeming in different collateral ratio settings:

## Collateral Whitelist The Parallizer can handle assets requiring permissioned holders. Certain collateral assets can be whitelisted, meaning only specific addresses are allowed to burn them for stablecoins or receive them during redemptions. This is particularly relevant for security tokens with restricted transferability. The presence of whitelisted assets limits the full functionality and fairness of Parallelizer to whitelisted addresses only. For example, if whitelisted collateral represents 20% of a fully collateralized protocol, a non-whitelisted address redeeming stablecoins would only receive 80% of the equivalent value (as they cannot receive the whitelisted token), whereas a whitelisted address would receive 100%. Non-whitelisted addresses can still burn stablecoins for non-whitelisted collateral. Since redemption is primarily intended for sophisticated market makers and arbitrageurs (who are likely to be whitelisted), incorporating whitelisted collateral adds complexity to the redemption process but does not hinder Parallelizer’s ability to maintain the stablecoin’s price parity with its reserves on the secondary market. Whitelist management can vary depending on the asset and is typically overseen by protocol governance or external trusted systems.