diff options
| -rw-r--r-- | R/tranche_functions.R | 31 |
1 files changed, 21 insertions, 10 deletions
diff --git a/R/tranche_functions.R b/R/tranche_functions.R index c167384..217a7b3 100644 --- a/R/tranche_functions.R +++ b/R/tranche_functions.R @@ -31,13 +31,16 @@ GHquad <- function(n){ return(result)
}
-#' Basic recursive algorithm of Andersen, Sidenius and Basu
+#' Loss distribution of a portfolio
#'
#' \code{lossdistrib} computes the probability distribution of a sum
#' of independent Bernouilli variables with unequal probabilities.
#'
+#' This uses the basic recursive algorithm of Andersen, Sidenius and Basu
+#' We compute the probability distribution of S = \sum_{i=1}^n X_i
+#' where X_i is Bernouilli(p_i)
#' @param p Numeric vector, the vector of success probabilities
-#' @return A vector such that q[k]=P(S=k)
+#' @return A vector q such that q[k]=P(S=k)
lossdistrib <- function(p){
## basic recursive algorithm of Andersen, Sidenius and Basu
n <- length(p)
@@ -50,11 +53,19 @@ lossdistrib <- function(p){ return(q)
}
+#' Loss distribution of a portfolio
+#'
+#' \code{lossdistrib.fft} computes the probability distribution of a sum
+#' of independent Bernouilli variables with unequal probabilities.
+#'
+#' This uses the fft. 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.
+#' It is slower than the recursive algorithm in practice.
+#' We compute the probability distribution of S = \sum_{i=1}^n X_i
+#' where X_i is Bernouilli(p_i)
+#' @param p Numeric vector, the vector of success probabilities
+#' @return A vector such that q[k]=P(S=k)
lossdistrib.fft <- function(p){
- ## computes loss distribution using the fft
- ## 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)
@@ -132,10 +143,10 @@ lossdistrib2.truncated <- function(p, w, S, N, cutoff=N){ recovdist <- function(dp, pp, w, S, N){
## computes the recovery distribution for a sum of independent variables
- ## R=\sum_{i=1}^n X_i
- ## where X_i = 0 w.p 1-dp[i]-pp[i]
- ## = w[i]*(1-S[i]) w.p dp[i]
- ## = w[i] w.p pp[i]
+ ## R=\sum_{i=1}^n w[i] X_i
+ ## where X_i = 0 w.p 1 - dp[i] - pp[i]
+ ## = 1 - S[i] w.p dp[i]
+ ## = 1 w.p pp[i]
## each non zero value v is interpolated on the grid as
## the pair of values floor(v/lu) and ceiling(v/lu) so that
## X_i has four non zero values
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