From c258ce56b223e8a0138a672b1be1cee22c468779 Mon Sep 17 00:00:00 2001
From: Guillaume Horel <guillaume.horel@serenitascapital.com>
Date: Mon, 18 Aug 2014 14:17:03 -0400
Subject: add a new method for skew mapping (probability matching)

---
 R/tranche_functions.R | 38 ++++++++++++++++++++++++++++++++------
 1 file changed, 32 insertions(+), 6 deletions(-)

(limited to 'R')

diff --git a/R/tranche_functions.R b/R/tranche_functions.R
index a436de9..ce39b16 100644
--- a/R/tranche_functions.R
+++ b/R/tranche_functions.R
@@ -692,30 +692,47 @@ BCtranche.pv <- function(index, protection=FALSE){
 }
 
 adjust.skew <- function(index1, index2, method="ATM"){
-    #index1 is the index of which we already have computed the skew
+    #index1 is the index for 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)
+    #    method="PM", do probability matching
+
     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))
     }
+    aux2 <- function(x, index1, skew, index2, K2){
+        return(abs(log(Probtrunc(index1, x, skew(x)))-
+                   log(Probtrunc(index2, K2, skew(x)))))
+    }
+    if(method %in% c("ATM", "TLP")){
+        el1 <- EL(index1)
+        el2 <- EL(index2)
+    }
+    skew <- splinefun(K1, index1$rho[-c(1, length(index1$rho))], "natural")
     if(method=="ATM"){
         K1eq <- el1/el2 * K2
     }else if(method == "TLP"){
         K1eq <- c()
+        m <- max(K2) + 0.3
         for(K2val in K2){
-            prog <- optimize(aux, interval=c(0,1),
+            prog <- optimize(aux, interval=c(0,m),
                              index1=index1, el1=el1, skew=skew,
                              index2=index2, el2=el2, K2=K2val)
             K1eq <- c(K1eq, prog$minimum)
         }
-    }
+    }else if (method=="PM"){
+        K1eq <- c()
+        m <- max(K2) + 0.3
+        for(K2val in K2){
+            prog <- optimize(aux2, interval=c(0, m),
+                             index1=index1, skew=skew, index2=index2, K2=K2val)
+            K1eq <- c(K1eq, prog$minimum)
+        }
+     }
     return(c(0, skew(K1eq), NA))
 }
 
@@ -810,6 +827,15 @@ ELtrunc <- function(index, K, rho){
     return( -tranche.pl(dist$L, index$cs, 0, K) )
 }
 
+Probtrunc <- function(index, K, rho){
+    dist <- BClossdistC(index$defaultprob, index$issuerweights, index$recov, rho, index$Z, index$w, index$N)
+    p <- cumsum(dist$L[,ncol(dist$L)])
+    support <- seq(0, 1, length=index$N)
+    probfun <- splinefun(support, p, method="hyman")
+    return(probfun(K))
+}
+
+
 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)
-- 
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