ASSET LEDGER
We define the Asset Ledger (AL) by firstly considering the deadband around the reference ratio:
LR3∈[rw,3(β)−dbL,3,rw,3(β)+dbU,3]: within swap deadband From before (§ Liquidity Risk Factor) LR3 is defined as:
When in equilibrium, the liquidity ratio is equal to its reference:
\begin{align*} \quad\quad\quad\quad LR_3 - [\, r_{w,3}(\text{β}) \,] &= 0 \\[4pt] \quad\quad\quad\quad \frac{AP + AR}{B} - [\, r_{w,3}(\text{β}) \,] &= 0 \\[4pt] \end{align*}
Define diff_ETH
as any ETH deposit or withdrawal from Taker’s Protect or Close, or credits or debits of ETH relating to a cross-side swap (see § Combining Differences).
AL:BAP+AR+diffETH−[rw,3(β)(±db∗,3)]
AL is positive when the liquidity ratio exceeds the reference ratio plus the deadband:
AL=(AP+AR+diffETH)−B⋅[−pbL,3(β)+pbU,3+dbU,3]:BAP+AR>[−pbL,3(β)+pbU,3+dbU,3] AL is negative when the liquidity ratio is lower than the reference ratio minus the deadband:
AL=(AP+AR+diffETH)−B⋅[−pbL,3(β)+pbU,3−dbL,3]:BAP+AR<[−pbL,3(β)+pbU,3−dbL,3] Otherwise, we set AL to zero:
AL=0:elsewhere CAPITAL LEDGER
We similarly define the Capital Ledger by firstly applying the deadband around the reference ratio:
LR13∈[rw,13(β)−dbL,13,rw,13(β)+dbU,13]: within swap deadband From § Liquidity Risk Factor, LR13 is defined as:
When in equilibrium, the liquidity ratio is equal to its reference:
LR13−[rw,13(β)](β⋅L+D+ECP+LCR)−[rw,13(β)]=0=0 We then define diffUSD as any USD deposit or withdrawal from Claim, Withdraw, or credits or debits of USD relating to a cross-side swap (see subsection Combining Differences).
CL:(β⋅L+D+ECP+diffUSD+LCR)−[rw,13(β)(±db∗,13)] CL is positive when the liquidity ratio exceeds the reference ratio plus the deadband:
CL=(CP+CR+diffUSD)(LR13−[pbL,13+pbU,13(β)+dbU,13])/LR13:LR13>[rw,13(β)+dbU,13] CL is negative when the liquidity ratio is lower than the reference ratio minus the deadband:
\begin{align*} CL &= -1 * (CP + CR + diff_{\text{USD}}) ([ pb_{L,\,13} + pb_{U,\,13}(\text{β}) - db_{L,\,13} ] \;-\; LR_{13}) / LR_{13}\\[8pt] &\;\;: \quad LR_{13} < [ r_{w,\,13}(\text{β}) - db_{L,\,13}] \end{align*}
Otherwise, we set CL to zero:
CL=0:elsewhere