diff options
Diffstat (limited to 'R/tranche_functions.R')
| -rw-r--r-- | R/tranche_functions.R | 69 |
1 files changed, 37 insertions, 32 deletions
diff --git a/R/tranche_functions.R b/R/tranche_functions.R index 83e7199..a436de9 100644 --- a/R/tranche_functions.R +++ b/R/tranche_functions.R @@ -691,18 +691,41 @@ BCtranche.pv <- function(index, protection=FALSE){ return(list(pl=plvec, cl=clvec, bp=bp))
}
-adjust.skew <- function(index, el1){
- el <- EL(index)
- K <- index$K[-c(1,length(index$K))]
- rhofun <- splinefun(K, index$rho[-c(1, length(index$rho))], "natural")
- K <- el/el1*K
- return(c(0, rhofun(K), NA))
+adjust.skew <- function(index1, index2, method="ATM"){
+ #index1 is the index of which we already have computed the skew
+ #index2 is the index we're mapping to
+ # if method="ATM", do simple at the money mapping
+ # method="TLP", do tranche loss proportion mapping
+ el1 <- EL(index1)
+ el2 <- EL(index2)
+ K1 <- index2$K[-c(1,length(index1$K))]
+ K2 <- index2$K[-c(1,length(index1$K))]
+ skew <- splinefun(K1, index1$rho[-c(1, length(index1$rho))], "natural")
+ aux <- function(x, index1, el1, skew, index2, el2, K2){
+ return(abs(ELtrunc(index1, x, skew(x))/el1-
+ ELtrunc(index2, K2, skew(x))/el2))
+ }
+ if(method=="ATM"){
+ K1eq <- el1/el2 * K2
+ }else if(method == "TLP"){
+ K1eq <- c()
+ for(K2val in K2){
+ prog <- optimize(aux, interval=c(0,1),
+ index1=index1, el1=el1, skew=skew,
+ index2=index2, el2=el2, K2=K2val)
+ K1eq <- c(K1eq, prog$minimum)
+ }
+ }
+ return(c(0, skew(K1eq), NA))
}
-theta.adjust.skew <- function(index, shortened=4){
+theta.adjust.skew <- function(index, shortened=4, method="ATM"){
#ajust the correlation skew by doing ATM mapping on the expected loss
- elshort <- EL(index, shortened=shortened)
- return(adjust.skew(index, elshort))
+ indexshort <- index
+ N <- nrow(index$cs)-shortened
+ indexshort$defaultprob <- indexshort$defaultprob[,1:N]
+ indexshort$cs <- indexshort$cs[1:N,]
+ return(adjust.skew(index, indexshort, method))
}
BCtranche.theta <- function(index, tradedate=Sys.Date(), shortened=4){
@@ -779,19 +802,12 @@ EL <- function(index, discounted=TRUE, shortened=0){ }
}
-ELtrunc <- function(index, K, rho, Z, w, Ngrid){
+ELtrunc <- function(index, K, rho){
## computes the expected loss of a portfolio below strike K
- ## could be written faster by using a truncated version of lossdistrib
+ ## could be written faster by using a truncated version of lossdist
## index should be a list with issuerweights, recov, defaultprob and cs parameters
- rho <- rep(rho, length(index$issuerweights))
- L <- matrix(0, Ngrid, dim(index$defaultprob)[2])
- L <- .C("BCloss_dist", index$defaultprob, dim(index$defaultprob)[1], dim(index$defaultprob)[2],
- as.double(index$issuerweights), as.double(index$recov), as.double(Z), as.double(w),
- as.integer(length(Z)), as.double(rho), as.integer(Ngrid), FALSE, L=L)$L
- support <- seq(0, 1, length=Ngrid)
- trancheloss <- pmin(support, K)
- ELvec <- crossprod(trancheloss, L)
- return( sum(index$cs$df * diff(c(0, as.numeric(ELvec)))) )
+ dist <- BClossdistC(index$defaultprob, index$issuerweights, index$recov, rho, index$Z, index$w, index$N)
+ return( -tranche.pl(dist$L, index$cs, 0, K) )
}
BCstrikes <- function(defaultprob, issuerweights, recov, cs, K, rho, Z, w, N=101) {
@@ -800,22 +816,11 @@ BCstrikes <- function(defaultprob, issuerweights, recov, cs, K, rho, Z, w, N=101 el <- EL(index)
ELvec <- c()
for(i in 2:length(K)){
- ELvec <- c(ELvec, ELtrunc(index, K[i], rho[i], Z, w, N))
+ ELvec <- c(ELvec, ELtrunc(index, K[i], rho[i]))
}
return( ELvec/el )
}
-skewmapping <- function(index1, rhofun, index2, K2, Z, w, N=101) {
- EL1 <- EL(index1)
- EL2 <- EL(index2)
- f <- function(x, ...){
- return(abs(ELtrunc(index1, x, rhofun(x), Z, w, N)/EL1-
- ELtrunc(index2, K2, rhofun(x), Z, w, N)/EL2))
- }
- return( optimize(f, interval=c(0,1), index1, rhofun, index2, K2, Z, w, N) )
-}
-
-
tranche.factor <- function(index){
## compute the factor to convert from delta on current notional to delta on original notional
## K1 and K2 original strikes
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