1 files changed, 42 insertions, 8 deletions
diff --git a/tranche_functions.R b/tranche_functions.R
index 3a5b568c..a7262ea0 100644
--- a/tranche_functions.R
+++ b/tranche_functions.R
@@ -279,7 +279,7 @@ tranche.cl <- function(L, R, cs, K1, K2, scaled=FALSE){
         support <- seq(0, 1, length=n)
         size <- K2 - K1 - crossprod(trancheloss(support, K1, K2), L) -
             crossprod(trancherecov(support, K1, K2), R)
-        sizeadj <-as.numeric(0.5 * (size + c(K2-K1, size[-length(size)])))
+        sizeadj <- as.numeric(0.5 * (size + c(K2-K1, size[-length(size)])))
         if(scaled){
             return( 1/(K2-K1) * crossprod(sizeadj * cs$coupons, cs$df) )
         }else{
@@ -311,6 +311,8 @@ tranche.pv <- function(L, R, cs, K1, K2){
 }
 
 adjust.attachments <- function(K, losstodate, factor){
+    ## computes the attachments adjusted for losses
+    ## on current notional
     return( pmin(pmax((K-losstodate)/factor, 0),1) )
 }
 
@@ -385,15 +387,47 @@ BCtranche.pv <- function(portfolio, index, coupon, K1, K2, rho1, rho2, lu=0.01){
 }
 
 BCtranche.delta <- function(portfolio, index, coupon, K1, K2, rho1, rho2, lu=0.01){
-    eps <- 1e-6
+    ## computes the tranche delta (on current notional) by doing a proportional
+    ## blip of all the curves
+    ## if K2==1, then computes the delta using the lower attachment only
+    ## this makes sense for bottom-up skews
+    eps <- 1e-4
     portfolioplus <- portfolio
     portfoliominus <- portfolio
     for(i in 1:length(portfolio)){
-        portfolioplus[[i]]@curve@hazardrates <- portfolioplus[[i]]@curve@hazardrates + eps
-        portfoliominus[[i]]@curve@hazardrates <- portfoliominus[[i]]@curve@hazardrates - eps
+        portfolioplus[[i]]@curve@hazardrates <- portfolioplus[[i]]@curve@hazardrates * (1 + eps)
+        portfoliominus[[i]]@curve@hazardrates <- portfoliominus[[i]]@curve@hazardrates * (1- eps)
     }
-    dPVtranche <- BCtranche.pv(portfolioplus, index, coupon, K1, K2, rho1, rho2, lu)$bp -
-        BCtranche.pv(portfoliominus, index, coupon, K1, K2, rho1, rho2, lu)$bp
-    dPVindex <- indexpv(portfolioplus, index)-indexpv(portfoliominus, index)
-    return( dPVtranche/(100*dPVindex))
+    dPVindex <- indexpv(portfolioplus, index) - indexpv(portfoliominus, index)
+    if(K2==1){
+        dPVtranche <- BCtranche.pv(portfolioplus, index, coupon, 0, K1, 0, rho1, lu)$bp -
+            BCtranche.pv(portfoliominus, index, coupon, 0, K1, 0, rho1, lu)$bp
+        K1adj <- adjust.attachments(K1, index$loss, index$factor)
+        delta <- (1 - dPVtranche/(100*dPVindex) * K1adj)/(1-K1adj)
+    }else{
+        dPVtranche <- BCtranche.pv(portfolioplus, index, coupon, K1, K2, rho1, rho2, lu)$bp -
+            BCtranche.pv(portfoliominus, index, coupon, K1, K2, rho1, rho2, lu)$bp
+        delta <- dPVtranche/(100*dPVindex)
+    }
+    ## dPVindex <- BCtranche.pv(portfolioplus, index, coupon, 0, 1, 0, 0.5, lu)$bp-
+    ##     BCtranche.pv(portfoliominus, index, coupon, 0, 1, 0, 0.5, lu)$bp
+    return( delta )
+}
+
+BCstrikes <- function(portfolio, index, coupon, K, rho) {
+    ## computes the strikes as a percentage of expected loss
+    EL <- c()
+    for(i in 2:length(K)){
+        EL <- c(EL, -BCtranche.pv(portfolio, index, coupon, K[i-1], K[i], rho[i-1], rho[i], lu)$pl)
+    }
+    Kmodified <- adjust.attachments(K, index$loss, index$factor)
+    return(cumsum(EL*diff(Kmodified))/sum(EL*diff(Kmodified)))
+}
+
+delta.factor <- function(K1, K2, index){
+    ## compute the factor to convert from delta on current notional to delta on original notional
+    ## K1 and K2 original strikes
+    factor <- (adjust.attachments(K2, index$loss, index$factor)
+               -adjust.attachments(K1, index$loss, index$factor))/(K2-K1)
+    return( factor )
 }