Under developing Page
The following describes how the flow actually takes place when the user enters each value such as a p e r p = E T H a m o u n t a_{perp}=ETH \ amount a p er p = ET H am o u n t a s q u a r t = S q u a r t a m o u n t a_{squart} = Squart \ amount a s q u a r t = Sq u a r t am o u n t
How to make Squart(√ETH)
First, the Uniswap v3 LP position shall be minted with the following Tokens:
r e q u i r e d e t h = a s q u a r t 2 ( 1 p − 1 p b ) required_{eth}=\frac{a_{squart}}{2}(\frac{1}{\sqrt{p}}-\frac{1}{\sqrt{p_b}}) re q u i re d e t h = 2 a s q u a r t ( p 1 − p b 1 )
r e q u i r e d u s d c = a s q u a r t 2 ( p − p a ) required_{usdc}=\frac{a_{squart}}{2}(\sqrt{p}-\sqrt{p_a}) re q u i re d u s d c = 2 a s q u a r t ( p − p a )
where, m = M a r g i n m= Margin m = M a r g in p = E T H p r i c e p= ETH \ price p = ET H p r i ce P a = L o w e r P r i c e r a n g e P_a = Lower Price_{range} P a = L o w er P r i c e r an g e P a = H i g e r P r i c e r a n g e P_a = Higer Price_{range} P a = H i g er P r i c e r an g e
In addition, add the following Token to retrieve Squart(√ETH).
o f f s e t e t h = a s q u a r t 2 1 p b offset_{eth}=\frac{a_{squart}}{2}\frac{1}{\sqrt{p_b}} o ff se t e t h = 2 a s q u a r t p b 1
o f f s e t u s d c = a s q u a r t 2 p a offset_{usdc}=\frac{a_{squart}}{2}\sqrt{p_a} o ff se t u s d c = 2 a s q u a r t p a
Therefore, the total Token amount of each of the above is required. See this Paper for detailed instructions.
Trading (entry position creation)
First, Exchange ETH and USDC with Uniswap.
S w a p p e d F o r S q u a r t = p ′ ∗ ( r e q u i r e d e t h + o f f s e t e t h ) SwappedForSquart=p'*(required_{eth} + offset_{eth}) Sw a pp e d F or Sq u a r t = p ′ ∗ ( re q u i re d e t h + o ff se t e t h )
e n t r y p e r p = p ′ ∗ a p e r p entry_{perp}=p'*a_{perp} e n t r y p er p = p ′ ∗ a p er p
e n t r y s q u a r t = r e q u i r e d u s d c + o f f s e t u s d c + S w a p p e d F o r S q u a r t entry_{squart}=required_{usdc}+offset_{usdc}+SwappedForSquart e n t r y s q u a r t = re q u i re d u s d c + o ff se t u s d c + Sw a pp e d F or Sq u a r t
where, p ′ = E T H P r i c e t r a d e p' = ETH \ Price_{trade} p ′ = ET H P r i c e t r a d e
Position's Value and Vault's Value
v p = p ∗ a p e r p − e n t r y p e r p + p ∗ a s q u a r t − e n t r y s q u a r t v_p=p * a_{perp} - entry_{perp} + \sqrt{p} * a_{squart} - entry_{squart} v p = p ∗ a p er p − e n t r y p er p + p ∗ a s q u a r t − e n t r y s q u a r t
V a u l t V a l u e = v p + m VaultValue = v_p + m Va u lt Va l u e = v p + m
Asset and Debt Concept
Treat the following as an ASSET for positive cases and a DEBT for negative cases.
a s s e t e t h = a p e r p + o f f s e t e t h asset_{eth} = a_{perp} + offset_{eth} a sse t e t h = a p er p + o ff se t e t h
a s s e t u s d c = − e n t r y p e r p − e n t r y s q u a r t + o f f s e t u s d c asset_{usdc}=-entry_{perp}-entry_{squart}+offset_{usdc} a sse t u s d c = − e n t r y p er p − e n t r y s q u a r t + o ff se t u s d c
As shown in this Paper , the OFFSET changes depending on the relocation of the range.
Reallocate Position
Protocol temporarily undertakes the liability when it relocates in place of User. This is expressed as Reallocation. The new debt needed at this time, or the debt to be returned, is as follows:
R e q u i r e d E T H = T o t a l S q u a r t A m o u n t 2 ( 1 p a p r e v − 1 p a c u r r e n t ) Required_{ETH}=\frac{TotalSquartAmount}{2}(\frac{1}{\sqrt{p_{a_{prev}}}}-\frac{1}{\sqrt{p_{a_{current}}}}) R e q u i re d ET H = 2 T o t a lSq u a r t A m o u n t ( p a p re v 1 − p a c u rre n t 1 )
R e q u i r e d U S D C = T o t a l S q u a r t A m o u n t 2 ( p b p r e v − p b c u r r e n t ) Required_{USDC}= \frac{TotalSquartAmount}{2}(\sqrt{p_{b_{prev}}}-\sqrt{p_{b_{current}}}) R e q u i re d U S D C = 2 T o t a lSq u a r t A m o u n t ( p b p re v − p b c u rre n t )
On the next trade, the debt is transferred to the trader by updating the offset.
o f f s e t e t h ← o f f s e t e t h + a s q u a r t 2 ( 1 p a p r e v − 1 p a c u r r e n t ) offset_{eth} ← offset_{eth} + \frac{a_{squart}}{2}(\frac{1}{\sqrt{p_{a_{prev}}}}-\frac{1}{\sqrt{p_{a_{current}}}}) o ff se t e t h ← o ff se t e t h + 2 a s q u a r t ( p a p re v 1 − p a c u rre n t 1 )
o f f s e t u s d c ← o f f s e t u s d c + a s q u a r t 2 ( p b p r e v − p b c u r r e n t ) offset_{usdc} ← offset_{usdc} + \frac{a_{squart}}{2}(\sqrt{p_{b_{prev}}}-\sqrt{p_{b_{current}}}) o ff se t u s d c ← o ff se t u s d c + 2 a s q u a r t ( p b p re v − p b c u rre n t )
The interest payments that occur while the protocol is shouldering the debt accumulate as ReallocationFeeGrowth.
Fee
This is expressed as a premium when considered as Option and as an interest rate when considered as Lending. The User earns Fee income from the Asset and pays a Fee on the Debt.
Debt Value
The settlement penalty is 0.05% of this debtValue.
Min Deposit
m i n V a l u e W i t h i n R a n g e = m i n ( v ( p R ) , v ( p R ) ) minValueWithinRange =min(v(pR), v(\frac{p}{R})) minVa l u e Wi t hin R an g e = min ( v ( pR ) , v ( R p ))
m i n D e p o s i t = P o s i t i o n V a l u e − m i n V a l u e W i t h i n R a n g e minDeposit = PositionValue - minValueWithinRange min De p os i t = P os i t i o nVa l u e − minVa l u e Wi t hin R an g e
Where, R = risk params and it sets as 1.2.
Liquidation Price
Find √X satisfy v x = m i n D e p o s i t v_x = minDeposit v x = min De p os i t
x 1 = ( − a s q u a r t + a s q u a r t 2 − a p e r p ∗ ( − e n t r y p e r p − e n t r y p e r p + m ) ) ∗ R 2 a p e r p \sqrt{x_1}=\frac{(-a_{squart}+\sqrt{a_{squart}^2-a_{perp}*(-entry_{perp}-entry_{perp}+m)}) * \sqrt{R}}{2a_{perp}} x 1 = 2 a p er p ( − a s q u a r t + a s q u a r t 2 − a p er p ∗ ( − e n t r y p er p − e n t r y p er p + m ) ) ∗ R
x 2 = ( − a s q u a r t − a s q u a r t 2 − a p e r p ∗ ( − e n t r y p e r p − e n t r y p e r p + m ) ) 2 a p e r p ∗ R \sqrt{x_2}=\frac{(-a_{squart}-\sqrt{a_{squart}^2-a_{perp}*(-entry_{perp}-entry_{perp}+m)})}{2a_{perp} * \sqrt{R}} x 2 = 2 a p er p ∗ R ( − a s q u a r t − a s q u a r t 2 − a p er p ∗ ( − e n t r y p er p − e n t r y p er p + m ) )
Margin Available
V a u l t V a l u e = M a r g i n + P o s i t i o n V a l u e Vault Value = Margin + Position Value Va u lt Va l u e = M a r g in + P os i t i o nVa l u e
M a r g i n U t i l i z i n g = M i n . D e p o s i t Margin Utilizing = Min. Deposit M a r g in U t i l i z in g = M in . De p os i t
M a r g i n A v a i l a b l e = V a u l t V a l u e − M a r g i n U t i l i z i n g MarginAvailable = VaultValue - Margin Utilizing M a r g in A v ai l ab l e = Va u lt Va l u e − M a r g in U t i l i z in g
W i t h d r a w − a b l e M a r g i n = m i n ( M a r g i n A v a i l a b l e , M a r g i n ) Withdraw-ableMargin=min(MarginAvailable, Margin) Wi t h d r a w − ab l e M a r g in = min ( M a r g in A v ai l ab l e , M a r g in )
