Formulas and Calculations

The Throttle Module relies on various formulas and calculations to achieve its functionality

Throttle function

t(r, s, m, \left(\frac{L}{D}, \frac{\Delta V_b}{\Delta V_s}\right)) \rightarrow (\Delta B, H) < (x, y)

Rule for comparing pairs is as following:

$\forall a, b, c, d \in \mathbb{Q},\ (a, b) < (c, d) \iff (a < b \text{ and } c < d)$

$r$ : Borrowing rate
$s$ : Throttle surcharge
$m$ : Multiplier on borrowing amount
$\frac{L}{D}$ : Potential liquidation amount at risk over market depth
$\frac{ΔV_b}{ΔV_s}$ : Rate of increase in borrowing velocity versus supply velocity
$(ΔB,H)$ : Output tuple representing delta in borrowing/supply and market health factor
$(x,y)$ : Threshold values for output control
$\mathbb{Q}$ is set of all rational numbers

This means that:

\text{Borrowing velocity, } V_b = \frac{\text{Net increase in borrowing (USD)}}{\text{Wallets transacted per epoch}}

\text{Supply velocity, } V_s = \frac{\text{Net increase in supply (USD)}}{\text{Wallets transacted per epoch}}

\Delta B = \text{Rate of change of } V_b, \quad \Delta S = \text{Rate of change of } V_s

\text{If } \frac{\Delta B}{\Delta S} \geq \text{Critical level} \Rightarrow r_{\text{new}} = m \cdot r + s

Where $r_{new}$ is a new borrow rate after applying multiplier and surcharge

If sudden 50% downside risk, then:

if\ \frac{P_{\text{at risk}}}{P_{\text{total}}} \lt x \Rightarrow \ no \ action \ needed \newline if \ x\leq \frac{P_{\text{at risk}}}{P_{\text{total}}} \lt y \Rightarrow adjust\ borrow/supply\ rates\ gradually+emit\ warnings \newline if\ \frac{P_{\text{at risk}}}{P_{\text{total}}} \geq y \Rightarrow adjust\ rates\ immediately\ and\ liquidate

Where:

$x$ - primary threshold

$y$ - secondary threshold

$P_{at-risk}$ - pool value at risk

$P_{total}$ - total value of pool

$x < y$

Adjusted\ borrow\ rate = Base\ Borrow\ Rate×(1+Multiplier×(\frac{ΔS}{ΔB}−CR))\\ + \ Surcharge

Last updated 1 year ago