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‎Docs/UserGuide/userguide.tex‎

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\newcommand{\SCVA}{\mathit{SCVA}}
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\newcommand{\bs}{\textbackslash}
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\newcommand{\REDY}{\color{red}Y}
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\newcommand{\IA}{\mathit{IA}}
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\newcommand{\Th}{\mathit{TH}}
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\newcommand{\CSA}{\mathit{CSA}}
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\begin{document}
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@@ -7549,28 +7552,31 @@ \subsection{Collateral Model}\label{sec:app_collateral}
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\begin{align}\label{eq:CSA}
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CSA(t_m) &=
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\begin{cases}
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\max(0, V_{set}(t_m) - I_A - T_{hold}),& V_{set}(t_m) - I_A \ge 0 \\
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\min(0, V_{set}(t_m) - I_A + T_{hold}),& V_{set}(t_m) - I_A < 0
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\max(0, \NPV(t_m) + \IA - \Th_{rec}),& \NPV(t_m) + \IA \ge 0 \\
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\min(0, \NPV(t_m) + \IA + \Th_{pay}),& \NPV(t_m) + \IA < 0
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\end{cases}
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\end{align}
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where
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\begin{itemize}
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\item $V_{set}(t_m)$ is the value of the netting set as of
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time $t_m$,
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\item $T_{hold}$ is the threshold exposure below which no collateral is
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required (possibly asymmetric),
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\item $\NPV(t_m)$ is the value of the netting set as of
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time $t_m$ from our persepctive,
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\item $\Th_{rec}$ is the threshold exposure below which we do not
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require collateral, likewise $\TH_{pay}$ is the threshold that applies to collateral posted to the counterparty,
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%\item $MTA$ is the minimum transfer amount for collateral margin
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% flow requests (possibly asymmetric)
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\item $I_A$ is the sum of all collateral independent amounts attached to
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the underlying portfolio of trades (positive amounts imply that the bank
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has received a net inflow of independent amounts from the
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\item $\IA$ is the sum of all collateral independent amounts attached to
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the underlying portfolio of trades (positive amounts imply that we
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have received a net inflow of independent amounts from the
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counterparty), assumed here to be cash.
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\end{itemize}
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As the collateral account already has a value of $C(t_m)$ at time $t_m$, the collateral shortfall is simply the
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difference between $C(t_m)$ and $CSA(t_m)$. However, we also need to account for the possibility that margin calls
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difference between $C(t_m)$ and $\CSA(t_m)$. However, we also need to account for the possibility that margin calls
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issued in the past have not yet been settled (for instance, because of disputes). If $M(t_m)$ denotes the net value of
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all outstanding margin calls at $t_m$, and $\Delta(t)$ is the difference $\Delta(t) = CSA(t_m) - C(t_m) - M(t_m)$
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all outstanding margin calls at $t_m$, and $\Delta(t)$ is the difference
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$$
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\Delta(t) = \CSA(t_m) - C(t_m) - M(t_m)
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$$
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between the {\em Credit Support Amount} and the current and outstanding collateral, then the actual margin
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\emph{Delivery Amount} $D(t_m)$ is calculated as follows:
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\begin{align}\label{eq:DA}
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0,& \left| \Delta(t) \right| < MTA
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\end{cases}
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\end{align}
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where $MTA$ is the minimum transfer amount.
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where $MTA$ is the minimum transfer amount.
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Consider the upper case of \eqref{eq:CSA}: If the initial value of the netting set is zero ($\NPV(t_0)=0$) and
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if $\Th_{rec}=0$, but the combined $\IA>0$, then the Credit Support Amount equals the Independent Amount, $\CSA(t_0)=\IA$.
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If moreover the initial collateral balance is zero (because the Independent Amount has not been received yet),
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then $\Delta(t_0)=\CSA(t_0)=\IA$, and the delivery amount $D(t_0)$ also matches the $\IA$ (assuming this exceeds the MTA),
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so that the next call leads to the transfer of the Independent Amount to us. For a positive $\Th_{rec}>0$, the transfer to us is reduced accordingly.
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In that case we can view the Independent Amount as an offset to the threshold.
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Consider the lower case of \eqref{eq:CSA}: If the netting set value is negative from our perspective and in absolute terms larger than the $\IA$,
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then the Credit Support Amount is just the negative difference $\CSA=-|\NPV| + \IA + \Th_{pay}$ so that we need to post collateral, but only the amount
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beyond the combined threshold $\IA + \Th_{pay}$.
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\subsubsection{Margin Period of Risk} \label{sec:mpor}
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After a counterparty defaults, it takes time to close out the portfolio. During this time period the portfolio value will change upon market conditions, therefore the portfolio's close-out value is subject to market risk, which is referred also as the close-out risk and the corresponding close-out period is called as the {\em Margin Period of Risk} (MPoR).

‎Examples/Example_1/ExpectedOutput/exposure_nettingset_CPTY_A.csv‎

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#NettingSet,Date,Time,EPE,ENE,PFE,ExpectedCollateral,BaselEE,BaselEEE
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CPTY_A,2016-02-05,0.000000,597.96,0.00,597.96,-597.96,597.96,597.96
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CPTY_A,2016-02-05,0.000000,597.96,0.00,597.96,597.96,597.96,597.96
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CPTY_A,2016-05-06,0.248634,127002.98,148662.15,560569.13,0.00,127643.44,127643.44
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CPTY_A,2016-08-05,0.497268,205715.45,254771.75,791661.75,0.00,207795.46,207795.46
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CPTY_A,2016-11-07,0.754098,287607.07,232717.91,1302106.25,0.00,291989.83,291989.83

‎Examples/Example_10/ExpectedOutput/collateral_iah_0/exposure_nettingset_CPTY_A.csv‎

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#NettingSet,Date,Time,EPE,ENE,PFE,ExpectedCollateral,BaselEE,BaselEEE
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CPTY_A,2016-02-05,0.000000,1201477.63,0.00,1201477.63,1201477.63,1201477.63,1201477.63
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CPTY_A,2016-02-19,0.038251,538979.96,599815.52,2031774.04,1201362.43,538955.11,1201477.63
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CPTY_A,2016-03-04,0.076503,499872.50,550606.59,1911931.64,1140368.01,499810.02,1201477.63
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CPTY_A,2016-03-18,0.114754,685247.21,366196.70,2616704.65,1089385.74,685098.66,1201477.63
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CPTY_A,2016-04-01,0.153005,481638.59,477144.87,2241395.38,1408138.10,481490.61,1201477.63
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CPTY_A,2016-04-15,0.191257,529941.55,524433.91,2036726.57,1412235.29,529728.11,1201477.63

‎Examples/Example_10/ExpectedOutput/collateral_iah_1/exposure_nettingset_CPTY_A.csv‎

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#NettingSet,Date,Time,EPE,ENE,PFE,ExpectedCollateral,BaselEE,BaselEEE
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CPTY_A,2016-02-05,0.000000,1201477.63,0.00,1201477.63,1201477.63,1201477.63,1201477.63
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CPTY_A,2016-02-19,0.038251,148204.16,1208943.84,1031950.21,2201266.55,148197.32,1201477.63
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CPTY_A,2016-03-04,0.076503,189966.02,1240601.78,912011.84,2140269.68,189942.28,1201477.63
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CPTY_A,2016-03-18,0.114754,241697.40,922542.26,1616917.06,2089281.11,241645.01,1201477.63
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CPTY_A,2016-04-01,0.153005,159755.38,1155155.09,1241341.54,2408031.54,159706.30,1201477.63
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CPTY_A,2016-04-15,0.191257,161278.02,1155654.84,1036559.88,2412119.75,161213.06,1201477.63

‎Examples/Example_10/ExpectedOutput/collateral_mpor/exposure_nettingset_CPTY_A.csv‎

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#NettingSet,Date,Time,EPE,ENE,PFE,ExpectedCollateral,BaselEE,BaselEEE
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CPTY_A,2016-02-05,0.000000,1201477.63,0.00,1201477.63,-1201477.63,1201477.63,1201477.63
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CPTY_A,2016-02-05,0.000000,1201477.63,0.00,1201477.63,1201477.63,1201477.63,1201477.63
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CPTY_A,2016-02-19,0.038251,475813.60,546273.05,1688515.02,1201370.26,475791.66,1201477.63
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CPTY_A,2016-03-04,0.076503,475068.76,378877.72,2176751.55,1130773.61,475009.37,1201477.63
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CPTY_A,2016-03-18,0.114754,708910.16,409660.47,2122672.25,1226788.43,708756.48,1201477.63

‎Examples/Example_10/ExpectedOutput/collateral_mta/exposure_nettingset_CPTY_A.csv‎

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#NettingSet,Date,Time,EPE,ENE,PFE,ExpectedCollateral,BaselEE,BaselEEE
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CPTY_A,2016-02-05,0.000000,1201477.63,0.00,1201477.63,-1201477.63,1201477.63,1201477.63
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CPTY_A,2016-02-05,0.000000,1201477.63,0.00,1201477.63,1201477.63,1201477.63,1201477.63
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CPTY_A,2016-02-19,0.038251,475813.60,546273.05,1688515.02,1201370.26,475791.66,1201477.63
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CPTY_A,2016-03-04,0.076503,476116.71,378813.98,2176928.89,1129661.91,476057.19,1201477.63
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CPTY_A,2016-03-18,0.114754,708621.22,409604.94,2122663.77,1227021.85,708467.60,1201477.63

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