Funding Curve

Each Funding Position receives funding fees determined by a dynamic funding rate. The funding rate follows a funding curve, which is a function of the Utilization Ratio.

• The Funding Curve is defined as a piecewise function with two segments.

• As the Utilization Ratio changes, the funding rate adjusts accordingly, ensuring a balanced relationship between Leveraged Position holders and Funding Position holders.

The Funding Rate is determined by a piecewise function of the Utilization Ratio (ur):

$$\begin{align*} &If\ ur < 80\%,\ Funding\ APY = a + b × ur \\ & If\ 80\% ≤ ur < 100\%,\ Funding\ APY = a + b × 80\% + c × (ur – 80\%)\\& a\ is\ the\ bottom\ funding \ rate,\ b\ is\ the\ first\ funding\ growth\ rate,\ c\ is\ the\ second\ funding\ growth\ rate.\end{align*}$$

Utilization Ratio:

The Utilization Ratio is a key metric that measures whether Leveraged Positions and Funding Positions in the market are balanced.

$$\begin{align*} &funding\ ratio = funding\ position\ in\ funding\ vault / total\ funding\ position\\ &leveraged\ ratio = leveraged\ position\ in\ leveraged\ vault / total\ leveraged\ position\end{align*}$$

When minting funding vault tokens is allowed:

$$Utilization\ Ratio= 0.5 + 0.5 * (leveraged\ ratio - funding\ ratio)$$

When minting funding vault tokens is not allowed:

$$Utilization\ Ratio= leveraged\ ratio$$

The Utilization Ratio is a key indicator that measures the balance between Leveraged Positions and Funding Positions in the market. It directly determines the value of the Funding APY.