Dynamic Increasing-only Floor Price

Lumi Finance’s unique rising-floor and protocol-owned liquidity are housed in its innovative AMM. Unlike traditional "constant product" pools with two separate token piles, this AMM holds a cash liquidity pool of various stable coins. It mints LUA when purchased and burns LUA when sold back.

The cash liquidity is distributed along a price curve, determining LUA's price for any order size. Buying LUA increases the price; selling decreases it. The difference between the spot price and the order price is called slippage. The price curve is a mathematical representation of LUA's buy/sell order slippage.

LUA price curve shows positive slippage up to a specific depth. Beyond this depth, the curve becomes flat, with zero slippage at the floor.

The curve's area underneath represents allocated cash liquidity for LUA. The x-axis is LUA's current supply, and the y-axis is the price. The green line indicates where selling LUA has slippage. Beyond the green area, slippage is zero, and LUA sells at the floor price.

LUA purchases add liquidity to the pool. When the sell-depth goes beyond a threshold, any new liquidity is considered "Additional Assets/Liquidity" and raises the floor.

In short, buying LUA increases the floor, locking in permanent gains.

Price raising algorithm

Market Liquidity, as illustrated by the blue area

Floor price liquidity as illustrated by the green area

Introducing a ratio called MFR:

MFR = Market Liquidity / Floor Price Liquidity Rate

The floor price can increase when the actual MFR reaches a specific threshold value, T%.

Upon reaching this trigger, the system transfers X% of liquidity from the market liquidity region (blue area) to the floor price zone (green area), resulting in (T - X)% remaining in the market liquidity region. Lumi Finance protocol sets its MFR target state to this value (T - X)%.

The threshold value T is determined by market forces, adjusting according to supply and demand. When the MFR threshold value T is reached, T increases to T + 0.25%. T decreases at a rate of 1% every 24 hours if T doesn't change at this period.

When a floor rising event occurs, the MFR is set to (T - X)% and T is incremented by an amount K.

For example, if T is 42%, X is 2%, and K is 0.25%, when the actual MFR reaches 42%, the system reduces it by 2%, reallocating that liquidity to the floor price zone and setting the actual MFR to 40%. T is then reset to 42.25%. If the price continues to climb and reaches T again, T will increase by another 0.25%.

Conversely, T also decreases over time at an initial rate of 1% per day. If the current MFR is at 40% and T is at 42%, T will make changes after 1 day. At this point, the MFR will be set to (40 - X)%, transferring 1% of liquidity to the floor price zone, and T will be increased to 41.25% ,a 0.25% increase as if the price had normally triggered it.

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