Slippage and Dynamic Swap Ratio

1. Slippage

• Slippage refers to the difference between the expected price and the actual transaction price in cryptocurrency trading. It can occur due to a lack of market liquidity, large transactions, or rapidly changing market conditions. To manage this volatility and provide users with a predictable trading experience, the DRESSdio Bridge sets a slippage tolerance of up to 2%.

$$Slippage Allowed=1±Slippage Percentage$$

• Slippage Tolerance: The slippage tolerance reflects the price difference that may occur during transaction execution. The bridge system applies this range in real-time during transaction execution to minimize user losses due to sudden price fluctuations.

2. Overview of the Dynamic Swap Ratio

• The dynamic swap ratio is the real-time calculated rate that reflects both market prices and fixed values when exchanging assets between the public chain (e.g., Polygon) and the private chain (Hyperledger Besu). This ratio accurately reflects market conditions, ensuring fairness in the exchange process.

$$\text{Swap Ratio} = \frac{P_{\text{swap}}}{P_{\text{DP}}}$$

• Dynamic Swap Ratio Calculation: The dynamic swap ratio is automatically adjusted based on real-time price data collected by the Oracle service, allowing users to trade at a fair exchange rate that reflects the latest market prices.

3. Final Swap Ratio Calculation

• The final swap ratio is calculated by integrating the slippage tolerance and the dynamic swap ratio. This determines the exchange rate at the actual time of the transaction, considering the slippage tolerance set by the user.

$$f(x) = \frac{P_{\text{swap}}}{P_{\text{DP}}} \times e^{\pm \alpha x}$$

• Final Swap Ratio Formula: This formula ensures that the dynamic swap ratio is adjusted within the slippage tolerance, guaranteeing that the transaction is completed within the range expected by the user.

• $f(x)$: A function representing the final swap ratio, calculated by considering slippage and the dynamic swap ratio.

• $P_{\text{swap}}$: Represents the adjusted price of the oracle price of the DRESS token on the listed exchange. It is calculated to reflect market data that is updated in real-time.

• $P_{\text{DP}}$: The fixed value of DP tokens, It is initially set at 0.01 USDT and it may be changed after prior notice depending on the price fluctuations in the physical market.

• $e$: The mathematical constant representing the base of the natural logarithm, approximately 2.718.

• $\pm$: Indicates that the price may rise or fall within the slippage range.

• $\alpha$: A constant representing the slippage tolerance, determined by the user-set slippage tolerance (e.g., 0.02, 2%).

• $x$: The adjustment value according to slippage, reflecting the variability within the slippage tolerance set by the user or calculated by the system.

4. Maximum Daily Swap Limit per User

• The maximum daily swap limit per user is a restriction set to prevent the depletion of the swap pool's liquidity, maintain system stability, and ensure that all users have a fair opportunity. This limit is calculated using the following formula, taking into account various market conditions:

• Formula for Maximum Daily Swap Limit per User: This formula combines two main elements to determine the daily swap limit per user. The first element is the allocation based on the fixed number of users, and the second element is the maximum swap ratio per user, set to prevent the liquidity pool from being rapidly depleted. Finally, this calculation considers the minimum guaranteed swap amount to ensure that users maintain a consistent platform experience.

$$\text{maximum daily swap limit per user} = \max\left(M_{\text{min}}, \min\left(\frac{L \times r}{n_{\text{user}}}, L \times r \times p_{\text{max}}\right)\right)$$

• $L$: Represents the total liquidity available in the swap pool, which is the total amount of swappable assets and can fluctuate in real-time.

• $r$: The maximum percentage of the entire swap pool that can be swapped in a day, set to protect pool liquidity while ensuring smooth transactions.

• $n_{\text{user}}$: The number of valid users, which is either a conservative estimate or the number of valid wallets holding tokens in DRESSdio Platform. This allows you to adjust your per-person quota based on the expected number of users.

• $p_{\text{max}}$: The maximum swap ratio per user, set to prevent any individual from monopolizing an excessive proportion of the liquidity pool.

• $M_{\text{min}}$: The minimum guaranteed swap amount per user, ensuring a basic level of trading functionality is maintained even if liquidity decreases.