Pools
Overview

# Pools

Capital is required for traders to get leverage on the platform. For this, there are Liquidity Pools(LPs): anyone can become a liquidity provider by depositing funds in the Liquidity Pool.

The profitability of LPs depends on the pool utilization ratio - the higher utilization, the higher interest rate. Each pool has an underlying asset and risk parameters such as: allowed trading tokens, allowed DEXes, stable coin pool, and others.

Currently pools use two points linear extrapolation for base interest rate calculation.

## Basic parameters

• EL(t) - expected liquidity
• B(t) - total borrowed
• r(t) - borrow rate
• d(t) - diesel rate
• CI(t) - cumulative index (it shows value of money at moment t)

### Periods and timestamp

All functions are piecewise linear functions. Each change in available liquidity or borrowed amount updates rate parameters. In follow formulas we use the convention:

$t_n - current\;timestamp,$
$t_{n-1} - timestamp\;of\;last\;rate\;update$

### Available liquidity

The amount of money available in pool.

### EL(t) - Expected Liquidity

The amount of money should be in the pool if all users close their Credit Accounts and return debt. If no action happens during $t_{n-1}$ and $t_n$, then the equation of $EL$ should be

$EL(t_{n})= EL(t_{n-1})+B(t_{n-1})*r(t_{n-1})*(t_{n}-t_{n-1})$

Beside, Add Liquidity and Remove Liquidity will have a new formula of $EL$.

### B(t) - Total borrowed

Represents total borrowed amount without accrued interest rate:

$B(t) = \sum b_i$

### r(t) - Borrow APY

Represents current borrow APY. Depends on pool utilisation parameter and computed independently using Interest rate model.

### d(t) Diesel rate

Liquidity providers get profits from holding diesel tokens because they grow with expected interest. LP can keep diesel tokens on their wallets and then withdraw the deposit + interest.

Diesel Rate is the price of Diesel token (LP token).

$d(t) = \frac{EL(t)}{diesel\;supply(t)}, \text{if diesel supply >0}$
$d(t) = 1, \text{if diesel supply is 0}$

### Cumulative Index

Cumulative Index is aggregated variable that shows value of borrowing money.

$CI(t_{n})=CI(t_{n-1})(1+r(t_{n-1})*(t_{n}-t_{n-1})),$
$r(t_{n})=calc\;interest\;rate(EL(t_{n}), available\;liquidity(t_n))$

### Rate parameters update

Updates borrow rate & cumulative index. Called each time when borrowed amount or available liquidity is changed:

$CI(t_{n})=CI(t_{n-1})(1+r(t_{n-1})*(t_{n}-t_{n-1})),$
$r(t_{n})=calc\;interest\;rate(EL(t_{n}), available\;liquidity(t_n))$