From 6b572b022895a93f8bd648b0f25d45ac419ea616 Mon Sep 17 00:00:00 2001
From: Guillaume Horel <guillaume.horel@serenitascapital.com>
Date: Fri, 27 Jun 2014 16:49:22 -0400
Subject: simplify code

---
 R/tranche_functions.R | 87 +++++++++++++++++++++------------------------------
 1 file changed, 35 insertions(+), 52 deletions(-)

diff --git a/R/tranche_functions.R b/R/tranche_functions.R
index 121df6a..469d68f 100644
--- a/R/tranche_functions.R
+++ b/R/tranche_functions.R
@@ -657,45 +657,51 @@ BClossdistC <- function(defaultprob, issuerweights, recov, rho, Z, w,
     return(list(L=r$L,R=r$R))
 }
 
-BCtranche.pv <- function(index, K1, K2, rho1, rho2,
-                         Z, w, N=length(index$issuerweights)+1, protection=FALSE){
+BCtranche.legs <- function(index, K, rho){
+    ## computes the protection leg and couponleg of a 0-K tranche
+    dist <- BClossdistC(index$defaultprob, index$issuerweights, index$recov, rho, index$Z, index$w, index$N)
+    return(list(cl=tranche.cl(dist$L, dist$R, index$cs, 0, K), pl=tranche.pl(dist$L, index$cs, 0, K)))
+}
+
+BCtranche.pv <- function(index, protection=FALSE){
     ## computes the protection leg, couponleg, and bond price of a tranche
     ## in the base correlation setting
-    if(K1==0){
-        if(rho1!=0){
-            stop("equity tranche must have 0 lower correlation")
-        }
-    }
-    dK <- K2 - K1
-    dist2 <- BClossdistC(index$defaultprob, index$issuerweights, index$recov, rho2, Z, w, N)
-    if(rho1!=0){
-        dist1 <- BClossdistC(index$defaultprob, index$issuerweights, index$recov, rho1, Z, w, N)
-    }
-    cl2 <- tranche.cl(dist2$L, dist2$R, index$cs, 0, K2)
-    cl1 <- tranche.cl(dist1$L, dist1$R, index$cs, 0, K1)
-    pl2 <- tranche.pl(dist2$L, index$cs, 0, K2)
-    pl1 <- tranche.pl(dist1$L, index$cs, 0, K1)
 
+    pl <- rep(0, length(index$rho)-1)
+    cl <- rep(0, length(index$rho)-1)
+    for(i in 2:(length(index$rho)-1)){
+        temp <- BCtranche.legs(index, index$K[i], index$rho[i])
+        pl[i] <- temp$pl
+        cl[i] <- temp$cl
+    }
+    dK <- diff(index$K)
+    plvec <- diff(pl)/dK[-length(dK)]
+    clvec <- diff(cl)/dK[-length(dK)]*index$tranche.running[-length(index$tranche.running)]
+    ## compute the supersenior as the left over
+    temp <- indexpv(index, tradedate = tradedate, clean = FALSE)
+    indexpl <- temp$pl
+    indexcl <- temp$cl/index$quotes$spread
+    plvec <- c(plvec, -(indexpl+pl[4])/dK[length(dK)])
+    clvec <- c(clvec, (indexcl-cl[4])*index$tranche.running[length(index$tranche.running)]/dK[length(dK)])
     if(protection){
-        bp <- (pl1-pl2+cl1-cl2)/dK
+        bp <- -plvec-clvec
     }else{
-        bp <- 100*(1-(pl2-pl1+cl2-cl1)/dK)
+        bp <- 1+plvec+clvec
     }
-    return(list(pl=(pl2-pl1)/dK, cl=(cl2-cl1)/dK, bp=bp))
+    return(list(pl=plvec, cl=clvec, bp=bp))
 }
 
-
 theta.adjust.skew <- function(index, shortened=4){
     #ajust the correlation skew by doing ATM mapping on the expected loss
     el <- EL(index)
-    elshort <- EL(index, shortened=4)
+    elshort <- EL(index, shortened)
     K <- index$K[-c(1,length(index$K))]
     rhofun <- splinefun(K, index$rho[-c(1, length(index$rho))], "natural")
     K <- el/elshort*K
-    return(rhofun(K))
+    return(c(0, rhofun(K)))
  }
 
-BCtranche.delta <- function(index, Z, w, N=length(index$portolio)+1, tradedate = Sys.Date()){
+BCtranche.delta <- function(index, tradedate = Sys.Date()){
     ## computes the tranche delta (on current notional) by doing a proportional
     ## blip of all the curves
     ## if K2==1, then computes the delta using the lower attachment only
@@ -720,39 +726,16 @@ BCtranche.delta <- function(index, Z, w, N=length(index$portolio)+1, tradedate =
     dPVindex1 <- indexpv(index.list[[2]], tradedate = tradedate, clean = FALSE)$bp-
         indexpv(index, tradedate = tradedate, clean = FALSE)$bp
 
-    index$cs$coupons <- index$cs$coupons/index$quotes$spread
-    cl <- matrix(0, length(index$rho)-2, length(index.list))
-    pl <-  matrix(0, length(index$rho)-2, length(index.list))
-    bp <- matrix(0, length(index$rho)-1, length(index.list))
-    for(i in 1:(length(index$rho)-2)){
-        dist.list <- list()
-        for(j in seq_along(index.list)){
-            dist.list[[j]] <- BClossdistC(index.list[[j]]$defaultprob,
-                                          index$issuerweights, index$recov, index$rho[i+1], Z, w, N)
-        }
-        for(j in seq_along(dist.list)){
-        #shock all the coupon and protection legs
-            cl[i,j] <- tranche.cl(dist.list[[j]]$L, dist.list[[j]]$R, index$cs, 0, index$K[i+1])
-            pl[i,j] <- tranche.pl(dist.list[[j]]$L, index$cs, 0, index$K[i+1])
-        }
+    bp <- matrix(0, length(index$K)-1, 4)
+    for(j in seq_along(index.list)){
+        temp <- BCtranche.pv(index.list[[j]])
+        bp[,j] <- temp$bp
     }
-    bp[1,] <- (pl[1,]+cl[1,]*index$tranche.running[1])
-    for(i in 2:(nrow(cl))){
-        bp[i,] <- pl[i,]-pl[i-1,]+(cl[i,]-cl[i-1,])*index$tranche.running[i]
-    }
-    bp[nrow(bp),] <- pl[nrow(pl),]+cl[nrow(cl),]*index$tranche.running[length(index$tranche.running)]
-    dPVtranche <- (bp[-nrow(bp),2]-bp[-nrow(bp),3])/diff(index$K[-length(index$K)])
-    dPVtranche2 <-  (bp[-nrow(bp),4] - bp[-nrow(bp),1])/diff(index$K[-length(index$K)])
+    dPVtranche <- bp[,2]-bp[,3]
+    dPVtranche2 <-  bp[,4] - bp[,1]
 
     deltas <- dPVtranche/dPVindex
     deltasplus <- dPVtranche2/dPVindex2
-    ##might need to check that in case of non 1 factor
-    deltas <- c(deltas,
-                (1-(bp[nrow(bp),2]-bp[nrow(bp),3])/dPVindex)/(1-index$K[length(index$K)-1]))
-    ##might need to check that in case of non 1 factor
-    deltasplus <- c(deltasplus,
-                    (1-(bp[nrow(bp),4]-bp[nrow(bp),1])/dPVindex2)/(1-index$K[length(index$K)-1]))
-
     gammas <- (deltasplus-deltas)/dPVindex1/100
 
     return( list(deltas=deltas, gammas=gammas) )
-- 
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