Protocol Math

Vault Ratio

The vault ratio is defined in the following way:

$$
\begin{gathered}
Let\\
C_a\, be\, the\, amount\, of\, collateral\, deposited \\
C_p\, be\, the\, price\, of\, the\, collateral\, \\
D_a\, be\, the\, amount\, of\, debt\, Minted\,\\
D_p\, be\, the\, price\, of\, the\, debt\, \\
V_r\, be \, the\, vault\, ratio\\
V_r =  \frac{C_a * C_p}{D_a * D_b} \times 100
\end{gathered}
$$ 

Liquidation

The Index token needed to liquidate a vault is:

$$
\begin{gathered}
Let\\
D_L \, be\, the\, amount\, of\, index\, token\, needed\, to\, liquidate\, a\, vault \\
L_p\, be\, the\, liquidation\, penalty\, \\
\\
D_L =  \frac{D_a\,D_p\,V_r - 100\,C_a\,C_p}{D_p (V_r - L_p - 100)}
\end{gathered}
$$

The reward received is given by:

$$
\begin{gathered}
Let\\
C_r \, be\, the\, amount\, of\, collateral\, received\, as\, reward\,\\
\\
C_r =  \frac{(D_a\,D_p\,V_r - 100\,C_a\,C_p)(L_p + 100)}{100\,C_p\,D_p (V_r - L_p - 100)}
\end{gathered}
$$

Fees

The mint fee and the fee are calculated in the following way:

$$
Let\, B_f\, be\, the\, burn\, fee\, percentage\\
Let\, M_f\, be\, the\, mint\, fee\, percentage\\
mintFee = \frac{C_a\,C_p\,M_f}{100\,E_p}\\
BurnFee = \frac{C_a\,C_p\,B_f}{100\,E_p}\\
$$

Math Derivation

For the derivation of the formulae please refer to this medium article