QPR-12277 fix the credit support amount, sign of independent amount

Author: pcaspers

Docs/UserGuide/userguide.tex

@@ -125,6 +125,9 @@
 \newcommand{\SCVA}{\mathit{SCVA}}
 \newcommand{\bs}{\textbackslash}
 \newcommand{\REDY}{\color{red}Y}
+\newcommand{\IA}{\mathit{IA}}
+\newcommand{\Th}{\mathit{TH}}
+\newcommand{\CSA}{\mathit{CSA}}
 
 \begin{document}
 
@@ -7549,28 +7552,31 @@ \subsection{Collateral Model}\label{sec:app_collateral}
 \begin{align}\label{eq:CSA}
 CSA(t_m) &= 
 \begin{cases}
-\max(0, V_{set}(t_m) - I_A - T_{hold}),& V_{set}(t_m) - I_A \ge 0 \\
-\min(0, V_{set}(t_m) - I_A + T_{hold}),& V_{set}(t_m) - I_A < 0
+\max(0, \NPV(t_m) + \IA - \Th_{rec}),& \NPV(t_m) + \IA \ge 0 \\
+\min(0, \NPV(t_m) + \IA + \Th_{pay}),& \NPV(t_m) + \IA < 0
 \end{cases}
 \end{align}
 where
 \begin{itemize}
-\item $V_{set}(t_m)$ is the value of the netting set as of
-  time $t_m$,
-  \item $T_{hold}$ is the threshold exposure below which no collateral is
-  required (possibly asymmetric),
+\item $\NPV(t_m)$ is the value of the netting set as of
+  time $t_m$ from our persepctive,
+  \item $\Th_{rec}$ is the threshold exposure below which we do not 
+  require collateral, likewise $\TH_{pay}$ is the threshold that applies to collateral posted to the counterparty,
 %\item $MTA$ is the minimum transfer amount for collateral margin
 %  flow requests (possibly asymmetric)
-\item $I_A$ is the sum of all collateral independent amounts attached to
-  the underlying portfolio of trades (positive amounts imply that the bank
-  has received a net inflow of independent amounts from the
+\item $\IA$ is the sum of all collateral independent amounts attached to
+  the underlying portfolio of trades (positive amounts imply that we
+  have received a net inflow of independent amounts from the
   counterparty), assumed here to be cash.
 \end{itemize}
 
 As the collateral account already has a value of $C(t_m)$ at time $t_m$, the collateral shortfall is simply the
-difference between $C(t_m)$ and $CSA(t_m)$. However, we also need to account for the possibility that margin calls
+difference between $C(t_m)$ and $\CSA(t_m)$. However, we also need to account for the possibility that margin calls
 issued in the past have not yet been settled (for instance, because of disputes). If $M(t_m)$ denotes the net value of
-all outstanding margin calls at $t_m$, and $\Delta(t)$ is the difference $\Delta(t) = CSA(t_m) - C(t_m) - M(t_m)$
+all outstanding margin calls at $t_m$, and $\Delta(t)$ is the difference 
+$$
+\Delta(t) = \CSA(t_m) - C(t_m) - M(t_m)
+$$
 between the {\em Credit Support Amount} and the current and outstanding collateral, then the actual margin
 \emph{Delivery Amount} $D(t_m)$ is calculated as follows:
 \begin{align}\label{eq:DA}
@@ -7580,7 +7586,18 @@ \subsection{Collateral Model}\label{sec:app_collateral}
 0,& \left| \Delta(t) \right| < MTA
 \end{cases}
 \end{align}
-where $MTA$ is the minimum transfer amount.
+where $MTA$ is the minimum transfer amount. 
+
+Consider the upper case of \eqref{eq:CSA}: If the initial value of the netting set is zero ($\NPV(t_0)=0$) and 
+if $\Th_{rec}=0$, but the combined $\IA>0$, then the Credit Support Amount equals the Independent Amount, $\CSA(t_0)=\IA$.
+If moreover the initial collateral balance is zero (because the Independent Amount has not been received yet),
+then $\Delta(t_0)=\CSA(t_0)=\IA$, and the delivery amount $D(t_0)$ also matches the $\IA$ (assuming this exceeds the MTA),
+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.
+In that case we can view the Independent Amount as an offset to the threshold.
+
+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 $\IA$, 
+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 
+beyond the combined threshold $\IA + \Th_{pay}$.
 
 \subsubsection{Margin Period of Risk} \label{sec:mpor}
 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_10/ExpectedOutput/collateral_iah_0/exposure_nettingset_CPTY_A.csv

@@ -0,0 +1,7 @@
+#NettingSet,Date,Time,EPE,ENE,PFE,ExpectedCollateral,BaselEE,BaselEEE
+CPTY_A,2016-02-05,0.000000,1201477.63,0.00,1201477.63,1201477.63,1201477.63,1201477.63
+CPTY_A,2016-02-19,0.038251,538979.96,599815.52,2031774.04,1201362.43,538955.11,1201477.63
+CPTY_A,2016-03-04,0.076503,499872.50,550606.59,1911931.64,1140368.01,499810.02,1201477.63
+CPTY_A,2016-03-18,0.114754,685247.21,366196.70,2616704.65,1089385.74,685098.66,1201477.63
+CPTY_A,2016-04-01,0.153005,481638.59,477144.87,2241395.38,1408138.10,481490.61,1201477.63
+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

@@ -0,0 +1,7 @@
+#NettingSet,Date,Time,EPE,ENE,PFE,ExpectedCollateral,BaselEE,BaselEEE
+CPTY_A,2016-02-05,0.000000,1201477.63,0.00,1201477.63,1201477.63,1201477.63,1201477.63
+CPTY_A,2016-02-19,0.038251,148204.16,1208943.84,1031950.21,2201266.55,148197.32,1201477.63
+CPTY_A,2016-03-04,0.076503,189966.02,1240601.78,912011.84,2140269.68,189942.28,1201477.63
+CPTY_A,2016-03-18,0.114754,241697.40,922542.26,1616917.06,2089281.11,241645.01,1201477.63
+CPTY_A,2016-04-01,0.153005,159755.38,1155155.09,1241341.54,2408031.54,159706.30,1201477.63
+CPTY_A,2016-04-15,0.191257,161278.02,1155654.84,1036559.88,2412119.75,161213.06,1201477.63