Mechanisms
Last updated
Last updated
Position Balance Rate First, imagine that the water level represents the relationship between the total value of LPs' short or long positions and the total liquidity they provide. When there is no addition or removal, the water level is flat, representing a perfect zero-sum, called the standard level (zero). Removing water lowers the level (negative value), and adding water raises it.
Relationship Between Water Level and Premium Rate The pool's water level (PR) height affects the price difference from the market's normal price (PPR). When zero-summed, the cost of water aligns with the market without a premium. The imbalance causes water prices to vary relative to the standard.
Price Calculation Imagine a calculator (ZSPM algorithm) that adjusts the water price based on the water level (position zero-sum rate) and other rules (system parameters) to ensure fairness in pricing, even with fluctuating member behaviors.
Adjustment Mechanism There are rules to automatically adjust the water price based on water level changes, ensuring the price aligns with market rates, even amid significant member activity fluctuations.
Conclusion A pond controlled by many people (LPs) has its water level (perpetual contract price) fluctuate with member activity. The goal is to stabilize the water level even when actions might induce changes. The water level balance reflects the relationship between the value of LPs' positions and their liquidity. A zero-summed water level means no change. The impact of water level on price differences (premium rate) depends on the zero-sum status. A calculator (ZSPM algorithm) adjusts prices based on water level and rules to maintain fairness. A rule system automatically adjusts prices to match the market, even during significant changes in member activity. In summary, this system maintains market-aligned prices through a rule-based algorithm that responds to changes in member behavior.
The core of the Zero Sum Position AMM is maintaining a balance between long and short positions. Therefore, whenever a trader opens a position, closes a position, or gets liquidated, the LP Pool will actively open or close a position in the opposite direction. The position balance rate (PR) is calculated as follows:
When the net short and long positions held by the LP Pool are zero, it indicates complete balance. If the LP Pool holds more long positions, the PR will be negative. The position balance affects the price (P) and is reflected through the Premium Multiplier (PM) parameter. The Premium Multiplier (PM) is defined as follows:
When PR is zero, PM is also zero, indicating position balance, and the price is exactly the same as the Oracle feed price (fP). Although ZSPM aims for position balance, it is practically impossible to maintain perfect balance. When an imbalance occurs, the contract price is shown as follows:
With the Oracle feed price (fP) and system parameters known, PM can reflect the position balance and thus the actual contract price.
The following explains the operation of PM = f(PR) using a transaction fee of 0.02% as an example.
PM = PMi
sp = System Parameters
LPV = Long Position Value
SPV = Short Position Value
Based on the above formula, 19 (PR, PM) coordinates are obtained as follows:
[(-50%, -10%), (-10%, -0.6%), (-9%, -0.5%), (-8%, -0.4%), (-7%, -0.3%), (-6%, -0.2%), (-5%, -0.15%), (-4%, -0.1%), (-2%, -0.05%), (0, 0), (2%, 0.05%), (4%, 0.1%), (5%, 0.15%), (6%, 0.2%), (7%, 0.3%), (8%, 0.4%), (9%, 0.5%), (10%, 0.6%), (50%, 10%)]
The following graph can be derived from these coordinates.
Using the 19 coordinates, we plot a curve composed of 18 line segments. Conceptually, this is similar to the Curve v2 stable swap, defining a premium range from -10% to +10%. Based on this function, we can calculate the current market price reflecting the position balance.
[*] For simplicity, the above coordinates have been simplified.
