| 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 |