There’s not much to this, it is simple supply/demand imbalance. If there is more supply than demand for DLLR then the price will fall below 1 USD, and vice versa, if there is more demand than supply then the price will go above 1 USD.
DLLR inherits the stability mechanisms of its underlying stablecoins, which are currently DOC and ZUSD.
With regards to the price floor: 1 DOC is redeemable for 1 USD of BTC as long as the amount-to-redeem is less than the value of nDOC₀ (a parameter in the Money On Chain protocol). And 1 ZUSD is redeemable for 1 USD of BTC minus a redemption fee (currently the redemption fee floor is 2.5%); so if the ZUSD redemption fee 2.5% this means 1 ZUSD (and, by proxy, 1 DLLR) has an effective floor price of 1 USD - 0.025 = 0.975 USD, beyond which it becomes profitable to redeem ZUSD for BTC and arb the price back up to the floor.
With regards to the price ceiling: 1 DOC can be minted by depositing 1 USD worth of BTC. So if the DOC (and, by proxy, the DLLR) price goes above 1 USD then it becomes profitable to mint 1 DOC, sell 1 USD worth, then keep the difference as profit. For the ZUSD ceiling, I’ll link my comment here which discusses this in detail.
The Sovryn AMM is not a stableswap AMM so it is going to have higher slippage on stablecoin pairs than if using an stableswap pool like Curve or Balancer. If/when BabelFish implements its basket balancing incentive algorithm we might see better pricing on stable pairs – TBD!