# 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_xwhere there are n Vaults
B_t	Total outstanding debt.	\displaystyle B_t=\sum^n_{i=0}BC_xwhere there are nVaults
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 + VTwhere 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 xwith 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