From 2776a1ad9bd9fd70c5cc098516ed9f3377d257e3 Mon Sep 17 00:00:00 2001
From: Guillaume Horel <guillaume.horel@serenitascapital.com>
Date: Wed, 25 Jun 2014 17:34:36 -0400
Subject: add function to theta adjust the skew

---
 R/tranche_functions.R | 25 +++++++++++++++++++------
 1 file changed, 19 insertions(+), 6 deletions(-)

diff --git a/R/tranche_functions.R b/R/tranche_functions.R
index ce08288..121df6a 100644
--- a/R/tranche_functions.R
+++ b/R/tranche_functions.R
@@ -684,6 +684,17 @@ BCtranche.pv <- function(index, K1, K2, rho1, rho2,
     return(list(pl=(pl2-pl1)/dK, cl=(cl2-cl1)/dK, 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)
+    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))
+ }
+
 BCtranche.delta <- function(index, Z, w, N=length(index$portolio)+1, tradedate = Sys.Date()){
     ## computes the tranche delta (on current notional) by doing a proportional
     ## blip of all the curves
@@ -709,7 +720,7 @@ BCtranche.delta <- function(index, Z, w, N=length(index$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$spreadref
+    index$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))
@@ -747,16 +758,18 @@ BCtranche.delta <- function(index, Z, w, N=length(index$portolio)+1, tradedate =
     return( list(deltas=deltas, gammas=gammas) )
 }
 
-EL <- function(index, discounted=TRUE){
+EL <- function(index, discounted=TRUE, shortened=0){
     ## computes the expected loss of a portfolio (time discounted if discounted is TRUE)
     ## given the default curves and recovery
     ## should be very close to the protection leg of the portfolio of cds
     ## index should be a list with issuerweights, recov, defaultprob and cs parameters
-    ELvec <- as.numeric(crossprod(index$issuerweights * (1-index$recov), index$defaultprob))
+    ## shortened: number of quarters to shorten the maturity by
+    Ncol <- ncol(index$defaultprob)-shortened
+    ELvec <- as.numeric(crossprod(index$issuerweights * (1-index$recov), index$defaultprob[,1:Ncol]))
     if(!discounted){
        return( diff(c(0, ELvec)) )
    }else{
-       return( sum(index$cs$df*diff(c(0, ELvec))) )
+       return( sum(index$cs$df[1:Ncol]*diff(c(0, ELvec))) )
    }
 }
 
@@ -778,10 +791,10 @@ ELtrunc <- function(index, K, rho, Z, w, Ngrid){
 BCstrikes <- function(defaultprob, issuerweights, recov, cs, K, rho, Z, w, N=101) {
     ## computes the strikes as a percentage of expected loss
     ## Kmodified is the current attachment points (adjusted for losses)
-    el <- EL(defaultprob, issuerweights, recov, cs)
+    el <- EL(index)
     ELvec <- c()
     for(i in 2:length(K)){
-        ELvec <- c(ELvec, ELtrunc(defaultprob, issuerweights, recov, cs, K[i], rho[i], Z, w, N))
+        ELvec <- c(ELvec, ELtrunc(index, K[i], rho[i], Z, w, N))
     }
     return( ELvec/el )
 }
-- 
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