Position Change Fee

Position change means any activity that changes the value of positions, including open, close or liquidate positions. Position change cause changes in naked positions.
The hAMM system has a special Position Change Fee (PCF) mechanism rewarding position changes that decrease naked positions, and discouraging position changes that increase naked positions.
When traders increase the naked positions of a certain derivative, they will pay extra PCF to the system, and on the flip side, receive PCF from the system.
The existence of PCF will encourage arbitrageurs to earn risk-free profit as follows: open a position under Derify protocol that is opposite to the naked position, then open a hedged position in an external market.
Such action is called "naked position arbitrage", which effectively takes naked position to external markets, and decreases the risk exposure of the system.
The existence of arbitrageurs will keep the value of naked position NNN
 close to zero, thus restricting naked position.
Liquidity Depth Factor
Liquidity Depth Factor (LDF) DDD
 is a function to position pool PPP
, the formula of which is as follows:
D=f(P)=min⁡(κ∗P, ψ)=min⁡(κ∗(Xall−Yall), ψ)D=\boldsymbol{f}(P)=\min{(\kappa*P,\ \psi)}=\min{\Big(\kappa*(X_{all}-Y_{all}),\ \psi\Big)}D=f(P)=min(κ∗P, ψ)=min(κ∗(Xall​−Yall​), ψ)
When the liquidity depth is limited, DDD
 equals risk sensitivity coefficient κ\kappaκ
 multiplied by position pool PPP
.
When the liquidity depth reached a certain threshold (κ∗P>ψ\kappa*P>\psiκ∗P>ψ
), DDD
 always equals to external liquidity depth simulator ψ\psiψ
.
Risk sensitivity coefficient κ\kappaκ
 is a pre-set constant. A smaller κ\kappaκ
 means the higher position pool PPP
 is needed to maintain the liquidity depth, i.e. the system is more sensitive.
External liquidity depth simulator ψ\psiψ
 is another constant, determined by the liquidity depth of external markets.
​κ\kappaκ
 and ψ\psiψ
 are changeable and can be adjusted via DAO community voting.
PCF Rates
PCF rates RRR
 is used to calculate the PCF, the formula of which is as follows:
R=ND=Xc+Ycmin⁡(κ∗(Xall−Yall), ψ)R=\dfrac{N}{D}=\dfrac{X_c+Y_c}{\min{\Big(\kappa*(X_{all}-Y_{all}),\ \psi\Big)}}R=DN​=min(κ∗(Xall​−Yall​), ψ)Xc​+Yc​​
​XXX
 is always positive and YYY
 is always negative.
The sign of RRR
 is determined by NNN
.
When NNN
 is positive:
naked position is long
PCF is positive
opening long position/closing short position shall pay PCF payment
opening short position/closing long position shall receive PCF rewards
When NNN
 is negative:
naked position is short
PCF is negative
opening short position/closing long position shall pay PCF payment
opening long position/closing short position shall receive PCF rewards
​RRR
 is a state of the system.
PCF Cost for A Transaction
PCF cost ccc
 for a transaction, means the PCF payable upon the transaction which shift the system naked position from NNN
 to N′N'N′
，and PCF rates from RRR
 to R′R'R′
. Assuming the position changed is Δp\Delta pΔp
,  it is calculated as follows:
c={−∣∣N′∣−∣N∣∣∗(∣R∣+∣R′∣2+ρ),∣R∣>∣R′∣0,∣R∣=∣R′∣∣∣N′∣−∣N∣∣∗(∣R∣+∣R′∣2+ρ),∣R∣<∣R′∣c=\begin{cases}
-\Big||N'|-|N|\Big|*\Big(\dfrac{|R|+|R'|}{2}+\rho\Big),&|R|>|R'|\\
\\
0,&|R|=|R'|\\
\\
\Big||N'|-|N|\Big|*\Big(\dfrac{|R|+|R'|}{2}+\rho\Big),&|R|<|R'|
\end{cases}c=⎩⎨⎧​−∣∣​∣N′∣−∣N∣∣∣​∗(2∣R∣+∣R′∣​+ρ),0,∣∣​∣N′∣−∣N∣∣∣​∗(2∣R∣+∣R′∣​+ρ),​∣R∣>∣R′∣∣R∣=∣R′∣∣R∣<∣R′∣​
The actual PCF fee is not correlated to the size and direction of Δp\Delta pΔp
 , but only related to the change of naked position (∣∣N′∣−∣N∣∣\Big||N'|-|N|\Big|∣∣​∣N′∣−∣N∣∣∣​
) and PCF rates (∣R∣|R|∣R∣
和∣R′∣|R'|∣R′∣
).
When ccc
 is positive, the trader pays a fee, when ccc
 is negative, the trader gets rewards.
​ρ\rhoρ
 is external arbitrage cost coefficient, to encourage external arbitrageurs by covering their slippage and trading cost when they doing the arbitrage. Generally, ρ\rhoρ
 = 0.1% may cover most of the arbitrage cost. ρ\rhoρ
 is changeable and can be adjusted via DAO community voting.
Risk Control
Position Restriction
Last modified 1mo ago