diff options
Diffstat (limited to 'calibrate_tranches.R')
| -rw-r--r-- | calibrate_tranches.R | 274 |
1 files changed, 0 insertions, 274 deletions
diff --git a/calibrate_tranches.R b/calibrate_tranches.R deleted file mode 100644 index 3e2599fc..00000000 --- a/calibrate_tranches.R +++ /dev/null @@ -1,274 +0,0 @@ -library("parallel")
-setwd("//WDSENTINEL/share/CorpCDOs/R")
-source("cds_utils.R")
-source("cds_functions_generic.R")
-source("index_definitions.R")
-source("tranche_functions.R")
-source("yieldcurve.R")
-source("optimization.R")
-
-cl <- makeCluster(6)
-
-MarkitData <- getMarkitIRData()
-L1m <- buildMarkitYC(MarkitData, dt = 1/12)
-L2m <- buildMarkitYC(MarkitData, dt = 1/6)
-L3m <- buildMarkitYC(MarkitData)
-L6m <- buildMarkitYC(MarkitData, dt = 1/2)
-setEvaluationDate(as.Date(MarkitData$effectiveasof))
-
-## calibrate HY19
-## calibrate the single names curves
-singlenames.data <- read.table(file="clipboard", sep="\t", header=T)
-nondefaulted <- singlenames.data[!singlenames.data$ticker %in% hy17$defaulted,]
-bps <- 1e-4
-
-cdsdates <- as.Date(character(0))
-for(tenor in paste0(1:5, "y")){
- cdsdates <- c(cdsdates, cdsMaturity(tenor))
-}
-
-## clusterEvalQ(cl, {setClass("abstractcurve")
-## setClass("defaultcurve", contains="abstractcurve",
-## representation(dates="Date", hazardrates="numeric"))
-## setClass("creditcurve", representation(issuer="character", startdate="Date",
-## recovery="numeric", curve="defaultcurve"))})
-## clusterExport(cl, list("nondefaulted", "cdsdates", "cdshazardrate", "today",
-## "bps", "couponSchedule", "nextIMMDate", "DiscountCurve", "L3m"))
-## test <- parSapply(cl, 1:nrow(nondefaulted), parf)
-
-## parf <- function(i){
-## SC <- new("creditcurve",
-## recovery=nondefaulted$recovery[i]/100,
-## startdate=today(),
-## issuer=as.character(nondefaulted$ticker[i]))
-## quotes <- data.frame(maturity=cdsdates, upfront = as.numeric(nondefaulted[i,5:9])*0.01,
-## running = rep(nondefaulted$running[i]*bps,5))
-## return( cdshazardrate(quotes, nondefaulted$recovery[i]/100))
-## }
-
-hy19portfolio <- c()
-for(i in 1:nrow(nondefaulted)){
- SC <- new("creditcurve",
- recovery=nondefaulted$recovery[i]/100,
- startdate=today(),
- issuer=as.character(nondefaulted$ticker[i]))
- quotes <- data.frame(maturity=cdsdates, upfront = as.numeric(nondefaulted[i,4:8])*0.01,
- running=rep(nondefaulted$running[i]*bps, 5))
- SC@curve <- cdshazardrate(quotes, nondefaulted$recovery[i]/100)
- hy19portfolio <- c(hy19portfolio, SC)
-}
-
-issuerweights <- rep(1/length(hy19portfolio), length(hy19portfolio))
-hy19$indexref <- 0.99
-hy19portfolio.tweaked <- tweakcurves(hy19portfolio, hy19)
-
-SurvProb <- SPmatrix(hy19portfolio.tweaked, hy19)
-## load common parameters
-K <- c(0, 0.15, 0.25, 0.35, 1)
-Kmodified <- adjust.attachments(K, hy19$loss, hy19$factor)
-tranche.upf <- c(37.5625, 87.25, 101.8125, 115.0625)
-tranche.running <- c(0.05, 0.05, 0.05, 0.05)
-
-Ngrid <- 2*nrow(nondefaulted)+1
-recov <- sapply(hy19portfolio.tweaked, attr, "recovery")
-cs <- couponSchedule(nextIMMDate(today()), hy19$maturity,"Q", "FIXED", 0.05, 0)
-
-## calibrate the tranches using base correlation
-rhovec <- c()
-f <- function(rho, ...){
- temp <- BClossdistC(SurvProb, issuerweights, recov, rho, Ngrid)
- bp <- 100*(1+1/(Kmodified[i]-Kmodified[i-1]) *
- (tranche.pv(temp$L, temp$R, cs, 0, Kmodified[i], Ngrid) -
- tranche.pv(oldtemp$L, oldtemp$R, cs, 0, Kmodified[i-1], Ngrid)))
- return( abs(tranche.upf[i-1]-bp))
-}
-
-for(i in 2:length(Kmodified)){
- rho <- optimize(f, interval=c(0,1),
- SurvProb, issuerweights, recov, Ngrid, tranche.upf, Kmodified, cs, oldtemp)$minimum
- oldtemp <- BClossdistC(SurvProb, issuerweights, recov, rho, Ngrid)
- rhovec <- c(rhovec, rho)
-}
-
-rhovec <- c(0, rhovec)
-deltas <- c()
-for(i in 2:5){
- deltas <- c(deltas, BCtranche.delta(hy19portfolio.tweaked, hy19, 0.05, K[i-1], K[i], rhovec[i-1], rhovec[i], Ngrid))
-}
-
-##calibrate by modifying the factor distribution
-bottomup <- 1:3
-topdown <- 2:4
-n.int <- 500
-n.credit <- length(hy19portfolio)
-errvec <- c()
-quadrature <- gauss.quad.prob(n.int, "normal")
-w <- quadrature$weights
-Z <- quadrature$nodes
-w.mod <- w
-defaultprob <- 1 - SurvProb
-p <- defaultprob
-rho <- 0.45
-
-clusterExport(cl, list("shockprob", "issuerweights", "rho", "Z", "lossrecovdist.term",
- "lossrecovdist", "lossdistC", "Ngrid",
- "tranche.pvvec", "tranche.pv", "tranche.pl", "tranche.cl",
- "trancheloss", "trancherecov", "pos", "Kmodified", "cs"))
-## TODO: investigate if this is the right thing w.r.t recovery
-parf <- function(i){
- pshocked <- apply(p, 2, shockprob, rho=rho, Z=Z[i])
- S <- 1 - Rstoch[i,,]
- dist <- lossrecovdist.term(pshocked,, issuerweights, S, Ngrid)
- return( tranche.pvvec(Kmodified, dist$L, dist$R, cs))
-}
-
-for(l in 1:100){
- Rstoch <- array(0, dim=c(n.int, n.credit, ncol(SurvProb)))
- for(t in 1:ncol(SurvProb)){
- for(i in 1:n.credit){
- Rstoch[,i,t] <- stochasticrecov(recov[i], 0, Z, w.mod, rho, defaultprob[i,t], p[i,t])
- }
- }
-
- clusterExport(cl, list("Rstoch", "p"))
- result <- parSapply(cl, 1:n.int, parf)
- ## solve the optimization problem
- program <- KLfit(100*(result[bottomup,]+1), w, tranche.upf[bottomup])
-
-
- err <- 0
- for(i in 1:n.credit){
- for(j in 1:ncol(p)){
- err <- err + abs(crossprod(shockprob(p[i,j], rho, Z), program$weight) - defaultprob[i,j])
- }
- }
- errvec <- c(errvec, err)
-
- ## update the new probabilities
- p <- MFupdate.prob(Z, program$weight, rho, defaultprob)
-
- errvec <- c(errvec, err)
- w.mod <- program$weight
- cat(err,"\n")
-}
-
-write.table(data.frame(Z=Z, w=w.mod), file=paste0("calibration-", Sys.Date(), ".csv"), col.names=T, row.names=F, sep=",")
-
-## computes MFdeltas
-newportf <- hy19portfolio.tweaked
-eps <- 1e-4
-for(i in 1:length(newportf)){
- newportf[[i]]@curve@hazardrates <- hy19portfolio.tweaked[[i]]@curve@hazardrates * (1 + eps)
-}
-SurvProb2 <- SPmatrix(newportf, hy19)
-p2 <- MFupdate.prob(Z, w.mod, rho, 1-SurvProb2)
-dPVtranches <- MFtranche.pv(cl, cs, w.mod, rho, 1-SurvProb2, p2, issuerweights) - MFtranche.pv(cl, cs, w.mod, rho, defaultprob, p, issuerweights)
-dPVindex <- indexpv(newportf, hy19)-indexpv(hy19portfolio.tweaked, hy19)
-MFdeltas <- dPVtranches/dPVindex
-
-#global deltas
-PVtranches <- MFtranche.pv(cl, cs, w.mod, rho, 1-SurvProb, p, issuerweights, Kmodified)
-pnlindex <- 1+t(PVtranches$pv.w)%*%diff(Kmodified)-hy19$indexref
-plot(1-cumsum(w.mod),PVindex, main="pnl of going long the index", xlab="Market factor cumulative probability distribution", type="l")
-pnltranches <- sweep(1+t(PVtranches$pv.w), 2, tranche.upf/100)
-matplot(1-cumsum(w.mod), pnltranches, 2, tranche.upf/100, main="pnl of going long the tranches", xlab="Market factor cumulative probability distribution", type="l")
-global.deltas <- rep(0,4)
-for(i in 1:4){
- global.deltas[i] <- lm(pnltranches[,i]~0+pnlindex, weights=w.mod)$coef
-}
-pnlhedged.model <- pnltranches-pnlindex%*%t(global.deltas)
-pnlhedged.market <- pnltranches-pnlindex%*%t(market.deltas)
-## generate a bunch of plots
-postscript("hedged tranches global.eps")
-matplot(1-cumsum(w.mod), pnlhedged.model, type="l", ylab="pnl of the hedged package (global deltas)", xlab="Market factor cumulative probability distribution")
-legend(0.35, y=0.75, c("0-15","15-25","25-35","35-100"), col=1:4, lty=1:4)
-dev.off()
-postscript("hedged tranches market.eps")
-matplot(1-cumsum(w.mod), pnlhedged.market, type="l", ylab="Pnl", main="pnl of the hedged package (market deltas)", xlab="Market factor cumulative probability distribution")
-legend(0.15, y=1.15, c("0-15","15-25","25-35","35-100"), col=1:4, lty=1:4)
-dev.off()
-postscript("0-15 hedged.eps")
-matplot(1-cumsum(w.mod), cbind(pnlhedged.model[,1], pnlhedged.market[,1]), type="l", ylab="Pnl", main="Pnl of the hedged package (market vs global deltas)\n 0-15 tranche", xlab="Market factor cumulative probability distribution")
-dev.off()
-postscript("15-25 hedged.eps")
-matplot(1-cumsum(w.mod), cbind(pnlhedged.model[,2], pnlhedged.market[,2]), type="l", ylab="Pnl", main="Pnl of the hedged package (market vs global deltas)\n 15-25 tranche", xlab="Market factor cumulative probability distribution")
-dev.off()
-postscript("25-35 hedged.eps")
-matplot(1-cumsum(w.mod), cbind(pnlhedged.model[,3], pnlhedged.market[,3]), type="l", ylab="Pnl", main="Pnl of the hedged package (market vs global deltas)\n 25-35 tranche", xlab="Market factor cumulative probability distribution")
-dev.off()
-postscript("35-100 hedged.eps")
-matplot(1-cumsum(w.mod), cbind(pnlhedged.model[,4], pnlhedged.market[,4]), type="l", ylab="Pnl", main="Pnl of the hedged package (market vs global deltas)\n 35-100 tranche", xlab="Market factor cumulative probability distribution")
-dev.off()
-
-## scenario based pricing
-## generate the scenarios by finding the quantiles of the loss and recovery distributions
-n.scenarios <- 100
-percentiles <- (seq(0, 1, length=n.scenarios+1)[-1]+
- seq(0, 1, length=n.scenarios+1)[-(n.scenarios+1)])/2
-l <- matrix(0, ncol(defaultprob), n.scenarios)
-r <- matrix(0, ncol(defaultprob), n.scenarios)
-
-MFdist <- MFlossdistrib(w.mod, rho, defaultprob, p, issuerweights, Ngrid)
-MFdist.orig <- MFlossdistrib(w, rho, defaultprob, defaultprob, issuerweights, Ngrid)
-lossdist.orig <- BClossdistC(SurvProb, issuerweights, recov, rho, 101, 500)
-for(i in 1:17){
- Lfun <- splinefun(c(0, cumsum(MFdist$L[,i])),c(0, seq(0, 1, length=Ngrid)), "monoH.FC")
- Rfun <- splinefun(c(0, cumsum(MFdist$R[,i])),c(0, seq(0, 1, length=Ngrid)), "monoH.FC")
- for(j in 1:99){
- l[i, j] <- Lfun(d1[j])
- r[i, j] <- Rfun(d1[j])
- }
-}
-
-## joint generation of scenarios for loss and recovery distribution
-clusterExport(cl, list("lossrecovdist.joint.term", "lossdistribC.joint"))
-MFdist2 <- MFlossdistrib2(cl, w.mod, rho, defaultprob, p, issuerweights, Ngrid)
-## memory never gets released by the clusters for some reasons, needs to call gc twice
-clusterCall(cl, gc)
-clusterCall(cl, gc)
-gc()
-#L+R<=1
-test <- apply(MFdist2[21,,], 2, rev)
-test.tri <- lower.tri(test)
-sum(test[test.tri])#close to 1
-
-## D=L+R
-dist <- MFdist2[21,,]
-supportD <- outer(seq(0,1, length=Ngrid), seq(0,1, length=Ngrid), "+")
-## compute the joint density of (L/D, D)
-## u=x/(x+y)
-## v=x+y
-x <- seq(0,1, length=Ngrid) %o% seq(0,1, length=Ngrid)
-y <- sweep(-x, 2, seq(0, 1, length=Ngrid), "+")
-xgrid <- round(x/0.005)
-ygrid <- round(y/0.005)
-distchv <- matrix(0, Ngrid, Ngrid)
-for(i in 1:Ngrid){
- for(j in 1:Ngrid){
- distchv[i,j] <- dist[xgrid[i,j]+1, ygrid[i,j]+1]*seq(0,1, length=Ngrid)[j]
- }
-}
-
-## compute reinvesting distribution
-beta <- 1.1
-f <- function(l, r)(1-l-r)/(1-r)^beta
-test <- outer(seq(0, 1, length=Ngrid), seq(0, 1, length=Ngrid), f)
-plot(density(x=test[-Ngrid*Ngrid], weights=dist[-Ngrid*Ngrid], from=0, to=5))
-
-## two dimensional scenarios
-n.scenarios <- 100
-percentiles <- (seq(0, 1, length=n.scenarios+1)[-1]+
- seq(0, 1, length=n.scenarios+1)[-(n.scenarios+1)])/2
-l <- matrix(0, ncol(defaultprob), n.scenarios)
-r <- matrix(0, ncol(defaultprob), n.scenarios)
-
-MFdist <- MFlossdistrib(w.mod, rho, defaultprob, p, issuerweights, Ngrid)
-i <- 21
-Lfun <- splinefun(c(0, cumsum(MFdist$L[,i])),c(0, seq(0, 1, length=Ngrid)), "monoH.FC")
-
-Rfun <- splinefun(c(0, cumsum(MFdist$R[,i])),c(0, seq(0, 1, length=Ngrid)), "monoH.FC")
- for(j in 1:99){
- l[i, j] <- Lfun(d1[j])
- r[i, j] <- Rfun(d1[j])
- }
-}
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