path: root/R/calibrate_tranches.R

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])
    }
}