# Nuon math spec

## Terminology

|Symbol|Domain|Name|Meaning|
|-|-|-|-|
|$p$|-|Nuon Position|-|
|$L_r(t)$|$\mathbb{R}_+$|Liquidation Ratio|-|
|$C_r(t; p)$|$\mathbb{R}_+$|Collateral Ratio|-|
|$K_\sigma$|$\mathbb{R}$|Volatility Constant|A pre-defined constant|
|$\epsilon_p(t)$|$\mathbb{R}$|Dynamic Peg Ratio|-|
|$P(t)$|$\mathbb{R_+}$|Nuon Market Price|-|
|$\bar{P}(t)$|$\mathbb{R_+}$|Nuon Target Price|-|
|$\pi(t, t-\Delta t)$|$\mathbb{R}$|Inflation|Correction from time $t-\Delta t$ to $t$. [Truflation](http://www.truflation.com/) is being used|

## Description

### Metrics

$\bar P(t) = \bar P(t-\Delta t) (1 + \pi(t, t-\Delta t))$
$\epsilon_p(t) = \frac{P(t) - \bar{P}(t)}{P(t)}$
$L_r(t) = \bar{P}(t)+K_\sigma+\epsilon_p(t)$

### Events

- Automatic Liquidation happens when $C_r(t; p) \le L_r(t)$
- Nuon actions: Mint and Burn