add function to theta adjust the skew

1 files 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 )

 }