From 6f4c38840d9fc2ebc7c909eeff418f97ba4a58a2 Mon Sep 17 00:00:00 2001
From: Guillaume Horel <guillaume.horel@serenitascapital.com>
Date: Mon, 16 Jun 2014 17:51:49 -0400
Subject: fix the deltas computation when non constant tranche spread

code is quite ugly, need to make it better
---
 R/tranche_functions.R | 59 +++++++++++++++++++++++++++++++++++++++------------
 1 file changed, 45 insertions(+), 14 deletions(-)

(limited to 'R/tranche_functions.R')

diff --git a/R/tranche_functions.R b/R/tranche_functions.R
index b21094f..2743efd 100644
--- a/R/tranche_functions.R
+++ b/R/tranche_functions.R
@@ -658,7 +658,7 @@ BClossdistC <- function(defaultprob, issuerweights, recov, rho, Z, w,
 }
 
 BCtranche.pv <- function(index, K1, K2, rho1, rho2,
-                         Z, w, N=length(index$issuerweights)+1){
+                         Z, w, N=length(index$issuerweights)+1, protection=FALSE){
     ## computes the protection leg, couponleg, and bond price of a tranche
     ## in the base correlation setting
     if(K1==0){
@@ -675,8 +675,13 @@ BCtranche.pv <- function(index, K1, K2, rho1, rho2,
     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)
-    return(list(pl=(pl2-pl1)/dK, cl=(cl2-cl1)/dK,
-                bp=100*(1+(pl2-pl1+cl2-cl1)/dK)))
+
+    if(protection){
+        bp <- (pl1-pl2+cl1-cl2)/dK
+    }else{
+        bp <- 100*(1-(pl2-pl1+cl2-cl1)/dK)
+    }
+    return(list(pl=(pl2-pl1)/dK, cl=(cl2-cl1)/dK, bp=bp))
 }
 
 BCtranche.delta <- function(index, Z, w, N=length(index$portolio)+1, tradedate = Sys.Date()){
@@ -706,22 +711,48 @@ BCtranche.delta <- function(index, Z, w, N=length(index$portolio)+1, tradedate =
         indexpv(index, tradedate = tradedate, clean = FALSE)$bp
     dPVindex1 <- indexpv(indexplus, tradedate = tradedate, clean = FALSE)$bp-
         indexpv(index, tradedate = tradedate, clean = FALSE)$bp
-    bpplus <- 0
-    bpminus <- 0
-    bp <- 0
-    bp2plus <- 0
+    clplus <- 0
+    clminus <- 0
+    cl <- 0
+    cl2plus <- 0
+    plplus <- 0
+    plminus <- 0
+    pl <- 0
+    pl2plus <- 0
+    bp <- c()
+    bpplus <- c()
+    bpminus <- c()
+    bp2plus <- c()
+    index$cs$coupons <- index$cs$coupons/index$spreadref
     for(i in 1:(length(index$rho)-2)){
         dist <- BClossdistC(index$defaultprob, index$issuerweights, index$recov, index$rho[i+1], Z, w, N)
         distplus <- BClossdistC(indexplus$defaultprob, index$issuerweights, index$recov, index$rho[i+1], Z, w, N)
         distminus <- BClossdistC(indexminus$defaultprob, index$issuerweights, index$recov, index$rho[i+1], Z, w, N)
         dist2plus <- BClossdistC(index2plus$defaultprob, index$issuerweights, index$recov, index$rho[i+1], Z, w, N)
-        bp <- c(bp, tranche.pv(dist$L, dist$R, index$cs, 0, index$K[i+1]))
-        bpplus <- c(bpplus, tranche.pv(distplus$L, distplus$R, index$cs, 0, index$K[i+1]))
-        bpminus <- c(bpminus, tranche.pv(distminus$L, distminus$R, index$cs, 0, index$K[i+1]))
-        bp2plus <- c(bp2plus, tranche.pv(dist2plus$L, dist2plus$R, index$cs, 0, index$K[i+1]))
-    }
-    dPVtranche <- 1/diff(index$K[-length(index$K)])*(diff(bpplus) - diff(bpminus))
-    dPVtranche2 <-  1/diff(index$K[-length(index$K)])*(diff(bp2plus) - diff(bp))
+        #shock all the coupon legs
+        cl <- c(cl, tranche.cl(dist$L, dist$R, index$cs, 0, index$K[i+1]))
+        clplus <- c(clplus, tranche.cl(distplus$L, distplus$R, index$cs, 0, index$K[i+1]))
+        clminus <- c(clminus, tranche.cl(distminus$L, distminus$R, index$cs, 0, index$K[i+1]))
+        cl2plus <- c(cl, tranche.cl(dist2plus$L, dist2plus$R, index$cs, 0, index$K[i+1]))
+        #shock all the protection legs
+        pl <- c(pl, tranche.pl(dist$L, index$cs, 0, index$K[i+1]))
+        plplus <- c(plplus, tranche.pl(distplus$L, index$cs, 0, index$K[i+1]))
+        plminus <- c(plminus, tranche.pl(distminus$L, index$cs, 0, index$K[i+1]))
+        pl2plus <- c(pl2plus, tranche.pl(dist2plus$L, index$cs, 0, index$K[i+1]))
+    }
+    for(i in 2:(length(cl))){
+        dK <- index$K[i]-index$K[i-1]
+        bp <- c(bp, (pl[i]+cl[i]*index$tranche.running[i]-(pl[i-1]+cl[i-1]*index$tranche.running[i]))/dK)
+        bpplus <- c(bpplus, (plplus[i]+clplus[i]*index$tranche.running[i]-
+                             (plplus[i-1]+clplus[i-1]*index$tranche.running[i]))/dK)
+        bpminus <- c(bpminus, (plminus[i]+clminus[i]*index$tranche.running[i]-
+                               (plminus[i-1]+clminus[i-1]*index$tranche.running[i]))/dK)
+        bp2plus <- c(bp2plus, (pl2plus[i]+cl2plus[i]*index$tranche.running[i]-
+                               (pl2plus[i-1]+cl2plus[i-1]*index$tranche.running[i]))/dK)
+
+    }
+    dPVtranche <- bpplus-bpminus
+    dPVtranche2 <-  bp2plus - bp
 
     deltas <- dPVtranche/dPVindex
     ##might need to check that in case of non 1 factor
-- 
cgit v1.2.3-70-g09d2