ASSET LEDGER
We define the Asset Ledger (AL ) by firstly considering the deadband around the reference ratio:
L R 3 ∈ [ r w , 3 ( β ) − d b L , 3 , r w , 3 ( β ) + d b U , 3 ] : within swap deadband LR_3 \;\in\; [\, r_{w,3}(\text{β}) - db_{L,3} \quad,\quad r_{w,3}(\text{β}) + db_{U,3} \,] \quad \text{: \; within swap deadband} L R 3 ∈ [ r w , 3 ( β ) − d b L , 3 , r w , 3 ( β ) + d b U , 3 ] : within swap deadband From before (§ Liquidity Risk Factor) LR3 is defined as:
( A P + A R ) / B (AP + AR)/B ( A P + A R ) / B
r w , 3 , t ( β t ) = − p b L , 3 ( β t ) + p b U , 3 ( ± d b ∗ , 3 ) r_{w,\,3,\,t}(\,\text{β}_t\,) = -\;pb_{L,\,3} (\,\text{β}_t\,) + pb_{U,\,3} \;\;\;\; (\;\pm\, db_{*,\,3}\,) r w , 3 , t ( β t ) = − p b L , 3 ( β t ) + p b U , 3 ( ± d b ∗ , 3 )
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).
A L : A P + A R + d i f f ETH B − [ r w , 3 ( β ) ( ± d b ∗ , 3 ) ] AL \quad:\quad \frac{AP + AR + diff_{\text{ETH}}}{B} \;-\; [\, r_{w,3}(\text{β}) \;\; (\;\pm\, db_{*,\,3}\,) \,] A L : B A P + A R + d i f f ETH − [ r w , 3 ( β ) ( ± d b ∗ , 3 ) ]
AL is positive when the liquidity ratio exceeds the reference ratio plus the deadband:
A L = ( A P + A R + d i f f ETH ) − B ⋅ [ − p b L , 3 ( β ) + p b U , 3 + d b U , 3 ] : A P + A R B > [ − p b L , 3 ( β ) + p b U , 3 + d b U , 3 ] \begin{align*}
AL &= \left(AP + AR + diff_{\text{ETH}}\right)
\;-\;
B \cdot \left[ -\, pb_{L,\,3}(\text{β}) + pb_{U,\,3} + db_{U,\,3} \right]\\[4pt]
&:\;\; \frac{AP + AR}{B} > \left[ -\, pb_{L,\,3}(\text{β}) + pb_{U,\,3} + db_{U,\,3} \right]
\end{align*} A L = ( A P + A R + d i f f ETH ) − B ⋅ [ − p b L , 3 ( β ) + p b U , 3 + d b U , 3 ] : B A P + A R > [ − p b L , 3 ( β ) + p b U , 3 + d b U , 3 ] AL is negative when the liquidity ratio is lower than the reference ratio minus the deadband:
A L = ( A P + A R + d i f f ETH ) − B ⋅ [ − p b L , 3 ( β ) + p b U , 3 − d b L , 3 ] : A P + A R B < [ − p b L , 3 ( β ) + p b U , 3 − d b L , 3 ] \begin{align*}
AL &= \left(AP + AR + diff_{\text{ETH}}\right)
\;-\;
B \cdot \left[ -\, pb_{L,\,3}(\text{β}) + pb_{U,\,3} - db_{L,\,3} \right]\\[4pt]
&:\;\; \frac{AP + AR}{B} < \left[ -\, pb_{L,\,3}(\text{β}) + pb_{U,\,3} - db_{L,\,3} \right]
\end{align*} A L = ( A P + A R + d i f f ETH ) − B ⋅ [ − p b L , 3 ( β ) + p b U , 3 − d b L , 3 ] : B A P + A R < [ − p b L , 3 ( β ) + p b U , 3 − d b L , 3 ] Otherwise, we set AL to zero:
A L = 0 : e l s e w h e r e \begin{align*}
AL &= 0 \\[6pt]
&\;\;:\;\; elsewhere
\end{align*} A L = 0 : e l se w h ere
CAPITAL LEDGER
We similarly define the Capital Ledger by firstly applying the deadband around the reference ratio:
L R 13 ∈ [ r w , 13 ( β ) − d b L , 13 , r w , 13 ( β ) + d b U , 13 ] : within swap deadband LR_{13} \;\in\; [\, r_{w,\,13}(\text{β}) - db_{L,\,13} \quad,\;\;\; r_{w,\,13}(\text{β}) + db_{U,\,13} \,] \quad \text{: \; within swap deadband} L R 13 ∈ [ r w , 13 ( β ) − d b L , 13 , r w , 13 ( β ) + d b U , 13 ] : within swap deadband From § Liquidity Risk Factor, LR13 is defined as:
( C P β ⋅ L + D + E + C R L ) (\frac{CP}{\text{β}\cdot L + D + E} + \frac{CR}{L}) ( β ⋅ L + D + E CP + L CR )
r w , 13 , t ( β t ) = p b L , 13 + p b U , 13 ( β t ) ( ± d b ∗ , 13 ) r_{w,\,13,\,t}(\,\text{β}_t\,) = \;pb_{L,\,13} + pb_{U,\,13}(\,\text{β}_t\,) \;\;\;\; (\;\pm\, db_{*,\,13}\,) r w , 13 , t ( β t ) = p b L , 13 + p b U , 13 ( β t ) ( ± d b ∗ , 13 )
When in equilibrium, the liquidity ratio is equal to its reference:
L R 13 − [ r w , 13 ( β ) ] = 0 ( C P β ⋅ L + D + E + C R L ) − [ r w , 13 ( β ) ] = 0 \begin{align*}
\quad\quad\quad\quad LR_{13} - [\, r_{w,\,13}(\text{β}) \,] &= 0 \\[4pt]
\quad\quad\quad\quad (\frac{CP}{\text{β}\cdot L + D + E} + \frac{CR}{L}) - [\, r_{w,\,13}(\text{β}) \,] &= 0 \\[4pt]
\end{align*} L R 13 − [ r w , 13 ( β ) ] ( β ⋅ L + D + E CP + L CR ) − [ r w , 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).
C L : ( C P + d i f f USD β ⋅ L + D + E + C R L ) − [ r w , 13 ( β ) ( ± d b ∗ , 13 ) ] CL \quad:\quad (\frac{\;CP + diff_{\text{USD}\;}}{\text{β}\cdot L + D + E} + \frac{CR}{L})
\;-\;
[\, r_{w,\,13}(\text{β}) \;\; (\;\pm\, db_{*,\,13}\,) \,] C L : ( β ⋅ L + D + E CP + d i f f USD + L CR ) − [ r w , 13 ( β ) ( ± d b ∗ , 13 ) ] CL is positive when the liquidity ratio exceeds the reference ratio plus the deadband:
C L = ( C P + C R + d i f f USD ) ( L R 13 − [ p b L , 13 + p b U , 13 ( β ) + d b U , 13 ] ) / L R 13 : L R 13 > [ r w , 13 ( β ) + d b U , 13 ] \begin{align*}
CL &= ( CP + CR + diff_{\text{USD}} )
( LR_{13} \;-\; [ pb_{L,\,13} + pb_{U,\,13}(\text{β}) + db_{U,\,13} ])
/ LR_{13}\\[8pt]
&\;\;: \quad LR_{13} > [ r_{w,\,13}(\text{β}) + db_{U,\,13}]
\end{align*} C L = ( CP + CR + d i f f USD ) ( L R 13 − [ p b L , 13 + p b U , 13 ( β ) + d b U , 13 ]) / L R 13 : L R 13 > [ r w , 13 ( β ) + d b U , 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:
C L = 0 : e l s e w h e r e \begin{align*}
CL &= 0 \\[6pt]
&\;:\;\; elsewhere
\end{align*} C L = 0 : e l se w h ere Last updated 6 months ago