Funding Rates

Funding rates act as a final controller to ensure our final objective
Residual risk 
While the AMM addresses the marginal risk from the change in inventory using premium and rebate, there remain some residual risks, one of which is caused by the change in the price process of the underlying asset. To cover for such risk, we charge funding periodically. 
Given Xt X_tXt​
 is a function of an nnn
 dimensional vector q\mathbf{q}q
, we need a way to define funding rate for each market such that the total funding accumulated across n nn
 markets add up to ρ(Xt+τ)−(P+L)\rho(X_{t+\tau})-(P+L)ρ(Xt+τ​)−(P+L)
. To achieve this, we use a risk attribution mechanism called Euler allocation. 
Let Xt,iX_{t,i}Xt,i​
 be the liability arising from iii
th market. Using Euler allocation, we calculate the amount of funding needed from iii
th market as ρEuler(Xt+τ,i∣Xt+τ)\rho_{Euler}(X_{t+\tau,i}|X_{t+\tau})ρEuler​(Xt+τ,i​∣Xt+τ​)
. Now, for each trader j∈Iij \in I_ij∈Ii​
 with position size qij∈Rq_{i_j} \in \mathbb{R}qij​​∈R
 where ∑j∈Iiqij=qi\sum_{j\in I_i}q_{i_j}=q_{i}∑j∈Ii​​qij​​=qi​
, they are responsible for covering 
ρEuler(Xt+τ,i∣Xt+τ)qijqi\rho_{Euler}(X_{t+\tau,i}|X_{t+\tau})\frac{q_{i_j}}{q_{i}}ρEuler​(Xt+τ,i​∣Xt+τ​)qi​qij​​​
For example, if the market is long-heavy (qi>0q_{i} > 0qi​>0
), traders with long position (qij>0)(q_{i_j}>0)(qij​​>0)
 pays funding, while those with short position (qij<0)(q_{i_j}< 0)(qij​​<0)
 receives funding. This way, the AMM accumulates F=∑i=1n∑j∈IiρEuler(Xt+τ,i∣Xt+τ)qijqi=ρ(Xt+τ)−(P+L)F=\sum_{i=1}^n\sum_{j\in I_i}\rho_{Euler}(X_{t+\tau,i}|X_{t+\tau})\frac{q_{i_j}}{q_{i}}=\rho(X_{t+\tau})-(P+L)F=∑i=1n​∑j∈Ii​​ρEuler​(Xt+τ,i​∣Xt+τ​)qi​qij​​​=ρ(Xt+τ​)−(P+L)
, which is precisely the amount of funding needed to satisfy the invariant Xt+τ≤P+L+FX_{t+\tau}\leq P+L+FXt+τ​≤P+L+F
 with high probability.
Premiums / Rebates
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Risk Engine
Last modified 3mo ago