diff options
Diffstat (limited to 'R/tranche_functions.R')
| -rw-r--r-- | R/tranche_functions.R | 42 |
1 files changed, 33 insertions, 9 deletions
diff --git a/R/tranche_functions.R b/R/tranche_functions.R index 4d5abab..c167384 100644 --- a/R/tranche_functions.R +++ b/R/tranche_functions.R @@ -10,6 +10,18 @@ ## - do the correlation adjustments when computing the deltas since it seems to be
## the market standard
+#' Gauss-Hermite quadrature weights
+#'
+#' \code{GHquad} computes the quadrature weights for integrating against a
+#' Gaussian distribution.
+#'
+#' if f is a function, then with(GHquad(100), crossprod(f(Z), w))
+#'
+#' @param n Integer, the number of nodes
+#' @return A list with two components:
+#' \item{Z}{the list of nodes}
+#' \item{w}{the corresponding weights}
+#'
GHquad <- function(n){
n <- as.integer(n)
Z <- double(n)
@@ -19,6 +31,13 @@ GHquad <- function(n){ return(result)
}
+#' Basic recursive algorithm of Andersen, Sidenius and Basu
+#'
+#' \code{lossdistrib} computes the probability distribution of a sum
+#' of independent Bernouilli variables with unequal probabilities.
+#'
+#' @param p Numeric vector, the vector of success probabilities
+#' @return A vector such that q[k]=P(S=k)
lossdistrib <- function(p){
## basic recursive algorithm of Andersen, Sidenius and Basu
n <- length(p)
@@ -36,19 +55,24 @@ lossdistrib.fft <- function(p){ ## complexity is of order O(n*m)+O(m*log(m))
## where m is the size of the grid and n the number of probabilities.
## this is slower than the recursive algorithm
+ n <- length(p)
theta <- 2*pi*1i*(0:n)/(n+1)
Phi <- 1 - p + p%o%exp(theta)
v <- apply(Phi, 2, prod)
return(1/(n+1)*Re(fft(v)))
}
+#' recursive algorithm with first order correction
+#'
+#' @param p Numeric, vector of default probabilities
+#' @param w Numeric, vector of weights
+#' @param S Numeric, vector of severities
+#' @param N Integer, number of ticks in the grid
+#' @param defaultflag Boolean, if True, we compute the default distribution
+#' (instead of the loss distribution).
+#' @return a Numeric vector of size \code{N} computing the loss (resp.
+#' default) distribution if \code{defaultflag} is FALSE (resp. TRUE).
lossdistrib2 <- function(p, w, S, N, defaultflag=FALSE){
- ## recursive algorithm with first order correction
- ## p vector of default probabilities
- ## w vector of weigths
- ## S vector of severities
- ## N number of ticks in the grid
- ## defaultflag if true computes the default distribution
n <- length(p)
lu <- 1/(N-1)
q <- rep(0, N)
@@ -366,11 +390,11 @@ lossrecovdist.joint.term <- function(defaultprob, prepayprob, w, S, N, defaultfl if(useC){
if(missing(prepayprob)){
for(t in 1:ncol(defaultprob)){
- Q[t,,] <- lossdistC.joint(defaultprob[,t], w, S[,t], N, defaultflag)
+ Q[t,,] <- lossdistC.jointblas(defaultprob[,t], w, S[,t], N, defaultflag)
}
}else{
for(t in 1:ncol(defaultprob)){
- Q[t,,] <- lossdistC.prepay.joint(defaultprob[,t], prepayprob[,t], w, S[,t], N, defaultflag)
+ Q[t,,] <- lossdistC.prepay.jointblas(defaultprob[,t], prepayprob[,t], w, S[,t], N, defaultflag)
}
}
}else{
@@ -913,7 +937,7 @@ Probtrunc <- function(index, K, rho){ }
-BCstrikes <- function(defaultprob, issuerweights, recov, cs, K, rho, Z, w, N=101) {
+BCstrikes <- function(index, K, rho) {
## computes the strikes as a percentage of expected loss
## Kmodified is the current attachment points (adjusted for losses)
el <- EL(index)
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