🧭Definitions

This page contains a table of definitions used to rigorously and unambiguously define key parts of protocol behavior, and may be updated from time to time.

Variable	Description	Notes
$B_p$​	Total outstanding principal.	$\displaystyle B_p=\sum^n_{i=0}BP_x$where there are ​$n$​ Vaults
$B_t$​	Total outstanding debt.	$\displaystyle B_t=\sum^n_{i=0}BC_x$​where there are $n$​Vaults
$C_{senior}$​	Cash balance of the senior tranche.	Balance of the senior tranche contract returned by the underlying ERC20 asset when balanceOf is called.
$C_{junior}$	Cash balance of the junior tranche.	Balance of the senior tranche contract returned by the underlying ERC20 asset when balanceOf is called.
$L_{senior}$​	Assets held by the senior tranche, including loans (principal).	$L_{senior} = C_{senior} + B_p$
$L_{junior}$​	Assets held by the junior tranche.	$L_{junior} = C_{junior}$
$U_{optimal}$	Optimal utilisation rate.	Percentage expressed in ray.
$U$​	Utilisation rate (actual).	$U = \begin{cases} 0\ & if\ L_{senior} = 0 \\ \frac{B_{t}}{L_{senior}}\ & else \end{cases}$
$R_{b}$	Base borrow rate.	The base interest rate. Set by governance.
$R_{slope1}$	Slope when $U > U_{optimal}$ ​	Set by governance.
$R^t_{s}$​	Current slope rate. New borrows receive this rate.	$R^{t}_{s} = \begin{cases} R_{b}, & if\ U \leq U_{optimal} \\ R_{b} + \frac{U}{U_{optimal}}R_{slope1}, & if\ U \gt U_{optimal} \end{cases}$
$\bar R_b$​	Average borrow APR	$\bar R_b = \displaystyle\frac{\sum_{i=0}^nR^n_i P_i}{B_p}$
$LiR_{optimal}$​	Optimal tranche liquidity ratio	Set by governance.
$LiR_t$​	Current tranche liquidity ratio	$\displaystyle LiR_{t} = \frac{L_{senior}}{L_{junior}}$​
$E(LiR)$​	Deviation of $LiR_t$ from $LiR_{optimal}$. Presently not in use.​	$E(LiR) = LiR_{optimal} - LiR_t$
$Y_{senior}$	Optimal senior yield allocation	Percentage, expressed in basis points.
$Y_{junior}$​	Optimal junior yield allocation	$1 - Y_{senior}$
​$Y_t$	Current actual income allocation, PID-like. Presently not in use.	$\displaystyle Y^t = \begin{cases} Y & if LiR_t = LiR_{s} \\ Y_{optimal} \cdot \displaystyle\frac{\displaystyle1}{\displaystyle1+\frac{E(LiR)}{LiR_{optimal}}} & if E(LiR) \gt 0 \\ Y_{optimal} \cdot 1+\displaystyle\frac{E(LiR)}{LiR_{optimal}} & if E(LiR) \lt 0 \end{cases}$​
$R_l$​	Current lender interest rate	$R_l = R_bU$​
$R_{senior}$	Senior tranche effective interest rate	$R_{senior} = R_l \cdot Y_{senior}$​
$R_{junior}$​	Junior tranche effective interest rate	$R_{junior} = R_l\cdot Y_{junior}\cdot LiR_{t}$​
$S_{senior}$​	Total supply of senior tranche shares	vToken totalSupply()
$S_{junior}$	Total supply of junior tranche shares	vToken totalSupply()
$Ex(t)$​	Exchange rate of shares to the underlying asset	$Ex(x)=L_x/S_x$ where $x$ is one of junior or senior
$FV_o$​	Asset floor price at purchase block height	Provided by Oracle
$FV_t$​	Asset floor price at current block height	Provided by Oracle
$GAV_x$	Gross asset value of a Vault $x$, by current floor price. Presently not in use.	$GAV_x = \Sigma_{i \in liens}FV_t + VT$where $liens$ is the set of unredeemed non-fungible assets​ in the Vault.
$VT_x$​	Underlying ERC20 balance for a Vault $x$.	Return value of balanceOf()
$DR_{\alpha}$​	A drawdown by a Vault.	$DR_{\alpha} = (P,R,Term,Epoch,NPer,Pmt)$​
$P_\alpha$​	Principal component of a drawdown $DR_{\alpha}$​	-
$R_\alpha$​	Interest rate applied to $DR_{\alpha}$.​	$R_\alpha = R^t_s$ where $R^t_s$ is the prevailing slope rate at time of origination $t$​
$I_\alpha$​	Interest component of $DR_{\alpha}$.	$I_\alpha=R_\alpha P_\alpha$​
$Term_\alpha$​	The loan term of $DR_{\alpha}$ in seconds.	Always a multiple of $T_{month}$.​
$Epoch_\alpha$​	The payment interval of $DR_{\alpha}$ in seconds.	Always a multiple of $T_{month}$​
$EPY(\alpha)$​	Number of payment intervals per year for $DR_{\alpha}$​.	$\displaystyle EPY(\alpha)=\frac{T_{year}}{Epoch_\alpha}$
$NPer(\alpha)$​	Number of instalments needed to repay the principal and interest for $DR_{\alpha}$.​	$NPer(\alpha) = \displaystyle\frac{Term_\alpha}{Epoch_\alpha}$
$IPmt_i(\alpha)$​	Interest component of an instalment at period $i$​.	$\displaystyle IPmt_i(\alpha)=\frac{I(\alpha)}{NPer(\alpha)}$
$PPmt_i(\alpha)$​	Principal component of an instalment at period $i$​.	$\displaystyle PPmt_i(\alpha)=\frac{P_\alpha}{NPer(\alpha)}$​
$Pmt_i(\alpha)$	Total instalment amount at period $i$.	$Pmt_i(\alpha) = IPmt_i(\alpha)+PPmt_i(\alpha)$
$T^\alpha_{i}$​	Timestamp of due date of the next instalment of $DR_{\alpha}$​.	$T^\alpha_{i} = \begin{cases} T+Epoch_\alpha & if \ i = 0 \\ T^\alpha_{i-1}+Epoch_\alpha & else \end{cases}$​
$TPD(\alpha)$​	Time past due for $DR_{\alpha}$ expressed in seconds.	$TPD(\alpha) = \begin{cases} 0 & if \ T \leq T^\alpha_{i} \\ T - T^\alpha_{i} & else \end{cases}$​
$RE^t_\alpha$​	Total repayments made toward $DR_{\alpha}$​.	$\displaystyle RE^t_a = \sum_{i=1}^{n}Pmt(\alpha)$ where $n$ is the number of repayments that have been made.
$BC_x$​	Total debt of a Vault $x$, including interest.	$\displaystyle BC_x=\sum^{n}_{i=0} Pmt(i)$ for Vault $x$with $n$​ active Drawdowns.
$BP_x$​	Total principal debt of a Vault $x$	$\displaystyle BP_x=\sum^{n}_{i=0} P_i$ for Vault $x$​ with $n$​ active Drawdowns.
$BI_x$​	Total interest owed by a Vault $x$	$BI_x = BC_x-BP_x$
$B_{max}$​	Current Vault credit limit.	$B_{max} = max(FV_t \cdot (1 + \log_2(1+{Rep^x_v})), FV_t)$​
$LF$​	Liquidation threshold.	Currently set to $1$
$LB$​	Liquidation bonus.	Currently set to $0.1$
$LTV$​	Loan-to-value.	$HF = LTV\cdot LF$ Currently disabled.
$T$​	Current block timestamp	-
$T_{year}$​	Seconds per year	$31536000$
$T_{month}$	Seconds per month	$2592000$