Nothing
R/BondVal.Price.R
In BondValuation: Fixed Coupon Bond Valuation Allowing for Odd Coupon Periods and Various Day Count Conventions
Defines functions
BondVal.Price
Documented in
BondVal.Price
#' BondVal.Price (calculation of CP, AccrInt, DP, ModDUR, MacDUR and Conv)
#'
#' \bold{BondVal.Price} computes a bond's clean price given its yield.
#'
#' The function \bold{BondVal.Price} uses the function \bold{AnnivDates} to analyze the bond
#' and computes the clean price, the accrued interest, the dirty price and the sensitivity
#' measures modified duration (ModDUR), MacAulay duration (MacDUR) and convexity according
#' to the methodology presented in Djatschenko (2018).
#'
#' @param YtM The bond's yield to maturity p.a. on \code{SETT}. (required)
#' @param SETT The settlement date. Date class object with format "\%Y-\%m-\%d". (required)
#' @param Em The bond's issue date. Date class object with format "\%Y-\%m-\%d". (required)
#' @param Mat So-called "maturity date" i.e. date on which the redemption value and the final interest
#' are paid. Date class object with format "\%Y-\%m-\%d". (required)
#' @param CpY Number of interest payments per year (non-negative integer; element of the set
#' \{0,1,2,3,4,6,12\}. Default: 2.
#' @param FIPD First interest payment date after \code{Em}. Date class object with format "\%Y-\%m-\%d". Default: \code{NA}.
#' @param LIPD Last interest payment date before \code{Mat}. Date class object with format "\%Y-\%m-\%d". Default: \code{NA}.
#' @param FIAD Date on which the interest accrual starts (so-called "dated date"). Date class object with format "\%Y-\%m-\%d". Default: \code{NA}.
#' @param RV The redemption value of the bond. Default: \code{100}.
#' @param Coup Nominal interest rate per year in percent. Default: \code{NA}.
#' @param DCC The day count convention the bond follows. Default: \code{NA}.
#' For a list of day count conventions currently implemented type \code{View(List.DCC)}.
#' @param EOM Boolean indicating whether the bond follows the End-of-Month rule. Default: \code{NA}.
#' @param DateOrigin Determines the starting point for the daycount in "Date" objects.
#' Default: "1970-01-01".
#' @param InputCheck If 1, the input variables are checked for the correct format. Default: 1.
#' @param FindEOM If \code{TRUE}, \code{EOM} is overridden by the value inferred from the data.
#' Default: \code{FALSE}.
#' @param RegCF.equal If 0, the amounts of regular cash flows are calculated according to the
#' stipulated \code{DCC}. Any other value forces all regular cash flows to be equal sized.
#' Default: 0.
#' @param SimpleLastPeriod Specifies the interest calculation method in the final coupon period. Default: \code{TRUE}.
#' @param Calc.Method If 1, discount powers are computed with the same DCC as accrued interest.
#' If 0, discount powers are computed with DCC=2. Default: 1.
#' @param AnnivDatesOutput A list containing the output of the function AnnivDates. Default: \code{NA}.
#'
#' @return
#' \describe{
#' \item{CP}{The bond's clean price.}
#' \item{AccrInt}{The amount of accrued interest.}
#' \item{DP}{The bond's dirty price.}
#' \item{ytm.p.a.}{Annualized yield to maturity.}
#' \item{ModDUR.inYears}{Modified duration in years.}
#' \item{MacDUR.inYears}{MacAulay duration in years.}
#' \item{Conv.inYears}{Convexity in years.}
#' \item{ModDUR.inPeriods}{Modified duration in periods.}
#' \item{MacDUR.inPeriods}{MacAulay duration in periods.}
#' \item{Conv.inPeriods}{Convexity in periods.}
#' \item{tau}{Relative Position of the settlement date in regular periods.}
#' }
#'
#' @references
#' \enumerate{
#' \item{Djatschenko, Wadim, The Nitty Gritty of Bond Valuation: A Generalized Methodology for Fixed Coupon Bond Analysis Allowing for Irregular Periods and Various Day Count Conventions (November 5, 2018). Available at SSRN: https://ssrn.com/abstract=3205167.}
#' }
#'
#' @examples
#' data(PanelSomeBonds2016)
#' randombond<-sample(c(1:length(which(!(duplicated(PanelSomeBonds2016$ID.No))))),1)
#' df.randombond<-PanelSomeBonds2016[which(PanelSomeBonds2016$ID.No==randombond),]
#'
#' PreAnalysis.randombond<-suppressWarnings(AnnivDates(
#' unlist(df.randombond[
#' 1,c('Issue.Date','Mat.Date','CpY.Input','FIPD.Input','LIPD.Input',
#' 'FIAD.Input','RV.Input','Coup.Input','DCC.Input','EOM.Input')],
#' use.names=FALSE)))
#'
#' system.time(
#' for (i in c(1:nrow(df.randombond))) {
#' BondVal.Price.Output<-suppressWarnings(BondVal.Price(
#' unlist(
#' df.randombond[
#' i,c('YtM.Input','TradeDate','Issue.Date','Mat.Date','CpY.Input',
#' 'FIPD.Input','LIPD.Input','FIAD.Input','RV.Input','Coup.Input',
#' 'DCC.Input','EOM.Input')],use.names=FALSE),
#' AnnivDatesOutput=PreAnalysis.randombond))
#' df.randombond$CP.Out[i]<-BondVal.Price.Output$CP
#' }
#' )
#' plot(seq(1,nrow(df.randombond),by=1),df.randombond$CP.Out,"l")
#'
#' @export
#'
BondVal.Price<-function(YtM=as.numeric(NA),SETT=as.Date(NA),Em=as.Date(NA),Mat=as.Date(NA),CpY=as.numeric(NA),FIPD=as.Date(NA),LIPD=as.Date(NA),FIAD=as.Date(NA),RV=as.numeric(NA),Coup=as.numeric(NA),DCC=as.numeric(NA),EOM=as.numeric(NA),DateOrigin=as.Date("1970-01-01"),InputCheck=1,FindEOM=FALSE,RegCF.equal=0,SimpleLastPeriod=TRUE,Calc.Method=1,AnnivDatesOutput=as.list(NA)) {
if (length(YtM)>1) {
arglist<-YtM
argnames<-c("YtM","SETT","Em","Mat","CpY","FIPD","LIPD","FIAD","RV","Coup","DCC","EOM","DateOrigin","InputCheck","FindEOM","RegCF.equal","SimpleLastPeriod","Calc.Method")
for (i in c(1:length(arglist))) {
assign(argnames[i],arglist[i])
}
}
if (InputCheck==1) {
CheckedInput<-InputFormatCheck(YtM=YtM,SETT=SETT,Em=Em,Mat=Mat,CpY=CpY,FIPD=FIPD,LIPD=LIPD,FIAD=FIAD,RV=RV,Coup=Coup,DCC=DCC,EOM=EOM,DateOrigin=DateOrigin)
YtM<-CheckedInput$YtM
SETT<-CheckedInput$SETT
Em<-CheckedInput$Em
Mat<-CheckedInput$Mat
CpY<-CheckedInput$CpY
FIPD<-CheckedInput$FIPD
LIPD<-CheckedInput$LIPD
FIAD<-CheckedInput$FIAD
RV<-CheckedInput$RV
Coup<-CheckedInput$Coup
DCC<-CheckedInput$DCC
EOM<-CheckedInput$EOM
DateOrigin<-CheckedInput$DateOrigin
}
DP<-as.numeric(NA)
CP<-as.numeric(NA)
n<-as.numeric(NA)
k<-as.numeric(NA)
CN_tau<-as.numeric(NA)
tau<-as.numeric(NA)
w<-as.numeric(NA)
eta<-as.numeric(NA)
z<-as.numeric(NA)
AccrInt<-as.numeric(NA)
ModDUR.inYears<-as.numeric(NA)
MacDUR.inYears<-as.numeric(NA)
Conv.inYears<-as.numeric(NA)
ModDUR.inPeriods<-as.numeric(NA)
MacDUR.inPeriods<-as.numeric(NA)
Conv.inPeriods<-as.numeric(NA)
CF_final<-as.numeric(NA)
CF.remain<-as.numeric(NA)
DiscPowerVector<-as.numeric(NA)
PriceEqn<-as.numeric(NA)
if ((missing(YtM))|(is.na(YtM))) {
YtM<-as.numeric(NA)
warning("Yield to maturity (YtM) is missing or NA. NA created!")
} else {
if ((missing(SETT))|(is.na(SETT))) {
SETT<-as.Date(NA)
warning("Settlement date (SETT) is missing or NA. NA created!")
} else {
if ((SETT<Em)|(Mat<=SETT)) {
warning("Settlement date (SETT) is outside bond's lifespan. NA created!")
} else {
if (Calc.Method==0) {
RegCF.equal<-1
BondAnalysis<-suppressWarnings(AnnivDates(Em=Em,Mat=Mat,CpY=CpY,FIPD=FIPD,LIPD=LIPD,FIAD=FIAD,RV=RV,Coup=Coup,DCC=DCC,EOM=EOM,DateOrigin=DateOrigin,InputCheck=0,FindEOM=FindEOM,RegCF.equal=RegCF.equal))
} else {
if (all(is.na(AnnivDatesOutput))) {
BondAnalysis<-suppressWarnings(AnnivDates(Em=Em,Mat=Mat,CpY=CpY,FIPD=FIPD,LIPD=LIPD,FIAD=FIAD,RV=RV,Coup=Coup,DCC=DCC,EOM=EOM,DateOrigin=DateOrigin,InputCheck=0,FindEOM=FindEOM,RegCF.equal=RegCF.equal))
} else {
BondAnalysis<-AnnivDatesOutput
}
}
CpY<-BondAnalysis$Traits$CpY
RV<-BondAnalysis$Traits$Par
RealDates<-na.omit(BondAnalysis$DateVectors$RealDates)
if ((SETT<RealDates[1])|(SETT>=RealDates[length(RealDates)])) {
warning("Settlement date (SETT) is not between issue date (Em) and maturity date (Mat). NA created!")
} else {
if (is.na(BondAnalysis$Traits$FIPD)) {
FIPD<-BondAnalysis$Traits$est_FIPD
} else {
FIPD<-BondAnalysis$Traits$FIPD
}
if (is.na(BondAnalysis$Traits$LIPD)) {
LIPD<-BondAnalysis$Traits$est_LIPD
} else {
LIPD<-BondAnalysis$Traits$LIPD
}
DP.Output<-DP(RV,SETT,Em,Mat,CpY,FIPD,LIPD,FIAD,RV,Coup,DCC,EOM,DateOrigin,InputCheck=0,FindEOM,AnnivDatesOutput=BondAnalysis)
if (BondAnalysis$Warnings$ZeroFlag==1) {
Coup<-as.numeric(0)
CpY<-as.numeric(1)
}
AccrInt<-DP.Output[[2]]$Accrued_Interest
CF.values<-na.omit(BondAnalysis$PaySched$CoupPayments)
CF.dates<-na.omit(BondAnalysis$PaySched$CoupDates)
CF_List<-list(CF.values,CF.dates)
Use.ClosedForm<-as.numeric(0)
if (length(CF.values)>2) {
if (length(which(!duplicated(CF.values[-c(1,length(CF.values))])==TRUE))==1) {
Use.ClosedForm<-as.numeric(1)
}
}
if (Calc.Method==0) {
DCC_Orig<-DCC
DCC<-2
BondAnalysis<-suppressWarnings(AnnivDates(Em=Em,Mat=Mat,CpY=CpY,FIPD=FIPD,LIPD=LIPD,FIAD=FIAD,RV=RV,Coup=Coup,DCC=DCC,EOM=EOM,DateOrigin=DateOrigin,InputCheck=0,FindEOM=FindEOM,RegCF.equal=RegCF.equal))
}
# loading AnnivDates and expanding by one value to each side
AD.set<-na.omit(BondAnalysis$DateVectors$AnnivDates)
Refer<-BondAnalysis$Traits$Refer
AtomVector_Refer<-as.numeric(unlist(strsplit(as.character(Refer),split = "-")))
Atom1Refer<-AtomVector_Refer[1]
Atom2Refer<-AtomVector_Refer[2]
Atom3Refer<-AtomVector_Refer[3]
# creating the anniversary date preceding AD1
AtomVector_AD1<-as.numeric(unlist(strsplit(as.character(AD.set[1]),split = "-")))
Atom1AD1<-AtomVector_AD1[1]
Atom2AD1<-AtomVector_AD1[2]
Atom3AD1<-AtomVector_AD1[3]
PrevDate<-as.numeric(CppPrevDate(c(Atom1AD1,Atom2AD1,Atom3AD1,Atom1AD1,Atom2AD1,Atom3AD1,Atom1Refer,Atom2Refer,Atom3Refer,CpY,EOM)))
PrevDate<-as.Date(paste(PrevDate[1],PrevDate[2],PrevDate[3],sep="-"))
AD.set<-c(PrevDate,AD.set)
AD.set<-sort(na.omit(AD.set[!duplicated(AD.set)]))
# creating the anniversary date succeeding ADfin
AtomVector_ADfin<-as.numeric(unlist(strsplit(as.character(AD.set[length(AD.set)]),split = "-")))
Atom1ADfin<-AtomVector_ADfin[1]
Atom2ADfin<-AtomVector_ADfin[2]
Atom3ADfin<-AtomVector_ADfin[3]
SuccDate<-as.numeric(CppSuccDate(c(Atom1ADfin,Atom2ADfin,Atom3ADfin,Atom1ADfin,Atom2ADfin,Atom3ADfin,Atom1Refer,Atom2Refer,Atom3Refer,CpY,EOM)))
SuccDate<-as.Date(paste(SuccDate[1],SuccDate[2],SuccDate[3],sep="-"))
AD.set<-c(AD.set,SuccDate)
AD.set<-sort(na.omit(AD.set[!duplicated(AD.set)]))
AD.indexes<-na.omit(BondAnalysis$DateVectors$AD_indexes)
AD.indexes<-c((AD.indexes[1]-1),AD.indexes,(AD.indexes[length(AD.indexes)]+1))
SD.set<-na.omit(BondAnalysis$DateVectors$RealDates)
SD.indexes<-na.omit(BondAnalysis$DateVectors$RD_indexes)
AD_List<-list(AD.set,AD.indexes)
SD_List<-list(SD.set,SD.indexes)
### calculating tau
AtomVector_Mat<-as.numeric(unlist(strsplit(as.character(Mat),split = "-")))
Atom1Mat<-AtomVector_Mat[1]
Atom2Mat<-AtomVector_Mat[2]
Atom3Mat<-AtomVector_Mat[3]
AtomVector_PCD.SETT<-as.numeric(unlist(strsplit(as.character(PCD(SETT,AD.set)),split = "-")))
Atom1_PCD.SETT<-AtomVector_PCD.SETT[1]
Atom2_PCD.SETT<-AtomVector_PCD.SETT[2]
Atom3_PCD.SETT<-AtomVector_PCD.SETT[3]
AtomVector_SETT<-as.numeric(unlist(strsplit(as.character(SETT),split = "-")))
Atom1_SETT<-AtomVector_SETT[1]
Atom2_SETT<-AtomVector_SETT[2]
Atom3_SETT<-AtomVector_SETT[3]
AtomVector_NCD.SETT<-as.numeric(unlist(strsplit(as.character(NCD(SETT,AD.set)),split = "-")))
Atom1_NCD.SETT<-AtomVector_NCD.SETT[1]
Atom2_NCD.SETT<-AtomVector_NCD.SETT[2]
Atom3_NCD.SETT<-AtomVector_NCD.SETT[3]
AtomVector_NCD.NCD.SETT<-as.numeric(unlist(strsplit(as.character(NCD(NCD(SETT,AD.set),AD.set)),split = "-")))
Atom1_NCD.NCD.SETT<-AtomVector_NCD.NCD.SETT[1]
Atom2_NCD.NCD.SETT<-AtomVector_NCD.NCD.SETT[2]
Atom3_NCD.NCD.SETT<-AtomVector_NCD.NCD.SETT[3]
if (is.element(DCC,c(1,3,5,6,8,10,11,12,15))) {
tau_Num<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_SETT,Atom2_SETT,Atom3_SETT))[2]
tau_Den<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT))[2]
}
if (DCC==16) {
NonBus.PCD.SETT<-length(which((NonBusDays.Brazil$Date>=PCD(SETT,AD.set))&(NonBusDays.Brazil$Date<SETT)))
NonBus.PCD.NCD<-length(which((NonBusDays.Brazil$Date>=PCD(SETT,AD.set))&(NonBusDays.Brazil$Date<NCD(SETT,AD.set))))
tau_Num<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_SETT,Atom2_SETT,Atom3_SETT,NonBus.PCD.SETT))[2]
tau_Den<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,NonBus.PCD.NCD))[2]
}
if (DCC==2|DCC==14) {
OrigDCC<-DCC
DCC<-2
tau_Num<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,
Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_SETT,Atom2_SETT,Atom3_SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,
AD_List[[2]][which(AD_List[[1]]==PCD(SETT,AD.set))],
AD_List[[2]][which(AD_List[[1]]==NCD(PCD(SETT,AD.set),AD.set))],
CpY))[2]
tau_Den<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,
Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,Atom1_NCD.NCD.SETT,Atom2_NCD.NCD.SETT,Atom3_NCD.NCD.SETT,
AD_List[[2]][which(AD_List[[1]]==PCD(NCD(SETT,AD.set),AD.set))],
AD_List[[2]][which(AD_List[[1]]==NCD(PCD(SETT,AD.set),AD.set))],
CpY))[2]
DCC<-OrigDCC
}
if (DCC==4) {
tau_Num<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_SETT,Atom2_SETT,Atom3_SETT,Atom1_NCD.SETT,CpY))[2]
tau_Den<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,Atom1_NCD.NCD.SETT,CpY))[2]
}
if (DCC==7) {
tau_Num<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_SETT,Atom2_SETT,Atom3_SETT,Atom1Mat,Atom2Mat,Atom3Mat))[2]
tau_Den<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,Atom1Mat,Atom2Mat,Atom3Mat))[2]
}
if (is.element(DCC,c(9,13))) {
tau_Num<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_SETT,Atom2_SETT,Atom3_SETT,EOM))[2]
tau_Den<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,EOM))[2]
}
tau<-tau_Num/tau_Den+AD_List[[2]][which(AD_List[[1]]==PCD(SETT,AD.set))]
n<-SD.indexes[length(SD.indexes)-1]
l<-BondAnalysis$Traits$LCPLength
if ((!(is.na(LIPD)))&(SETT<LIPD)) {
k<-SD_List[[2]][which(SD_List[[1]]==NCD(SETT,SD.set))]
w<-k-tau
eta<-n-k
z<-l
CN_tau<-CF_List[[1]][which(CF_List[[2]]==NCD(SETT,SD.set))]
} else {
k<-n
w<-SD_List[[2]][which(SD_List[[1]]==NCD(SETT,SD.set))]-tau
eta<-0
z<-0
CN_tau<-0
}
###################>>>>>> <<<<<<<##########################################################
##############>>>>>> calculation of CP, ModDUR, MacDUR and Conv <<<<<<<#####################################################
###################>>>>>> <<<<<<<##########################################################
CF_final<-CF.values[length(CF.values)]+RV
if ((z==0)&(SimpleLastPeriod==TRUE)) { # simple interest
a<-1+YtM*w/(100*CpY)
DP<-CF_final/a
CP<-DP-AccrInt
ModDUR.inYears<-(-1)*(1/DP)*(-1)*CF_final*(a^(-2))*(w/CpY)
MacDUR.inYears<-ModDUR.inYears*a
Conv.inYears<-0.5*(1/DP)*2*CF_final*(a^(-3))*(w/CpY)^2
ModDUR.inPeriods<-ModDUR.inYears*CpY
MacDUR.inPeriods<-MacDUR.inYears*CpY
Conv.inPeriods<-Conv.inYears*(CpY^2)
} else {
a<-1+YtM/(100*CpY)
# if (round(a,8)==1) {
# CF.remain<-CF_List[[1]][which(CF_List[[2]]>SETT)]
# CF.remain<-c(CF.remain[-length(CF.remain)],CF.remain[length(CF.remain)]+RV)
# DP<-sum(CF.remain)
# CP<-DP-AccrInt
# } else {
#
# }
if ((Use.ClosedForm==1)&(!(round(a,8)==1))) {
CF<-CF.values[2]
DP<-(a^(-w))*(CN_tau+CF*(((a^eta)-1)/((a^eta)*(a-1)))+CF_final/(a^(eta+z)))
CP<-DP-AccrInt
ModDUR.inYears<-ModDUR(a,c(1,CN_tau,CF,CF_final,w,eta,z,CpY,DP))
# ModDUR.inYears<-(-1)*(1/DP)*dm_MyPriceEqn(a,c(1,CN_tau,CF,CF_final,w,eta,z,CpY))
MacDUR.inYears<-ModDUR.inYears*a
Conv.inYears<-CONV(a,c(2,CN_tau,CF,CF_final,w,eta,z,CpY,DP))
# Conv.inYears<-0.5*(1/DP)*dm_MyPriceEqn(a,c(2,CN_tau,CF,CF_final,w,eta,z,CpY))
ModDUR.inPeriods<-ModDUR.inYears*CpY
MacDUR.inPeriods<-MacDUR.inYears*CpY
Conv.inPeriods<-Conv.inYears*(CpY^2)
} else {
if (z>0) {
DiscPowerVector<-c((seq(0,eta,by=1)+w),(w+eta+z))
} else {
DiscPowerVector<-w
}
CF.remain<-CF_List[[1]][which(CF_List[[2]]>SETT)]
CF.remain<-c(CF.remain[-length(CF.remain)],CF.remain[length(CF.remain)]+RV)
# creating the price equation
summands<-gsub(" ","",paste(CF.remain,"/(a^",DiscPowerVector,")"))
PriceEqn<-paste(summands,collapse="+")
PriceFunction.Standard<-function(a) {
out<-eval(parse(text=PriceEqn))
return(out)
}
# creating the first derivative of the price function
d_PowerVector<-DiscPowerVector+1
d_summands<-gsub(" ","",paste("(-1)*(",CF.remain,"*",DiscPowerVector,"/(a^",d_PowerVector,"))"))
d_PriceEqn<-paste(d_summands,collapse="+")
d_PriceFunction.Standard<-function(a) {
out<-eval(parse(text=d_PriceEqn))
return(out)
}
DP<-PriceFunction.Standard(a)
CP<-DP-AccrInt
# calculating the Modified Duration and the MacAulay Duration
ModDUR.inPeriods<-(-1)*(1/DP)*d_PriceFunction.Standard(a)
MacDUR.inPeriods<-ModDUR.inPeriods*a
ModDUR.inYears<-ModDUR.inPeriods/CpY
MacDUR.inYears<-MacDUR.inPeriods/CpY
# calculating the Convexity
d2_PowerVector<-d_PowerVector+1
d2_summands<-gsub(" ","",paste("(",CF.remain,"*",DiscPowerVector,"*",d_PowerVector,")/(a^",d2_PowerVector,")"))
Added.d2_summands<-paste(d2_summands,collapse="+")
d2_PriceFunction.Standard <- function(a) {
out<-eval(parse(text=Added.d2_summands))
return(out)
}
Conv.inPeriods<-(1/DP)*0.5*d2_PriceFunction.Standard(a)
Conv.inYears<-Conv.inPeriods/(CpY^2)
}
}
}
}
}
}
# out<-list(tau=tau,n=n,k=k,w=w,eta=eta,z=z,CN_tau=CN_tau,ytm.p.a.=YtM,DP=DP,CF_final=CF_final,
# ModDUR.inPeriods=ModDUR.inPeriods,MacDUR.inPeriods=MacDUR.inPeriods,Conv.inPeriods=Conv.inPeriods,
# ModDUR.inYears=ModDUR.inYears,MacDUR.inYears=MacDUR.inYears,Conv.inYears=Conv.inYears,FIPD=FIPD,
# LIPD=LIPD)
# out<-Added.d2_summands
out<-list(CP=CP,AccrInt=AccrInt,DP=DP,ytm.p.a.=YtM,ModDUR.inYears=ModDUR.inYears,MacDUR.inYears=MacDUR.inYears,
Conv.inYears=Conv.inYears,ModDUR.inPeriods=ModDUR.inPeriods,MacDUR.inPeriods=MacDUR.inPeriods,
Conv.inPeriods=Conv.inPeriods,tau=tau)
return(out)
}
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Defines functions BondVal.Price
Documented in BondVal.Price
#' BondVal.Price (calculation of CP, AccrInt, DP, ModDUR, MacDUR and Conv)
#'
#' \bold{BondVal.Price} computes a bond's clean price given its yield.
#'
#' The function \bold{BondVal.Price} uses the function \bold{AnnivDates} to analyze the bond
#' and computes the clean price, the accrued interest, the dirty price and the sensitivity
#' measures modified duration (ModDUR), MacAulay duration (MacDUR) and convexity according
#' to the methodology presented in Djatschenko (2018).
#'
#' @param YtM The bond's yield to maturity p.a. on \code{SETT}. (required)
#' @param SETT The settlement date. Date class object with format "\%Y-\%m-\%d". (required)
#' @param Em The bond's issue date. Date class object with format "\%Y-\%m-\%d". (required)
#' @param Mat So-called "maturity date" i.e. date on which the redemption value and the final interest
#' are paid. Date class object with format "\%Y-\%m-\%d". (required)
#' @param CpY Number of interest payments per year (non-negative integer; element of the set
#' \{0,1,2,3,4,6,12\}. Default: 2.
#' @param FIPD First interest payment date after \code{Em}. Date class object with format "\%Y-\%m-\%d". Default: \code{NA}.
#' @param LIPD Last interest payment date before \code{Mat}. Date class object with format "\%Y-\%m-\%d". Default: \code{NA}.
#' @param FIAD Date on which the interest accrual starts (so-called "dated date"). Date class object with format "\%Y-\%m-\%d". Default: \code{NA}.
#' @param RV The redemption value of the bond. Default: \code{100}.
#' @param Coup Nominal interest rate per year in percent. Default: \code{NA}.
#' @param DCC The day count convention the bond follows. Default: \code{NA}.
#' For a list of day count conventions currently implemented type \code{View(List.DCC)}.
#' @param EOM Boolean indicating whether the bond follows the End-of-Month rule. Default: \code{NA}.
#' @param DateOrigin Determines the starting point for the daycount in "Date" objects.
#' Default: "1970-01-01".
#' @param InputCheck If 1, the input variables are checked for the correct format. Default: 1.
#' @param FindEOM If \code{TRUE}, \code{EOM} is overridden by the value inferred from the data.
#' Default: \code{FALSE}.
#' @param RegCF.equal If 0, the amounts of regular cash flows are calculated according to the
#' stipulated \code{DCC}. Any other value forces all regular cash flows to be equal sized.
#' Default: 0.
#' @param SimpleLastPeriod Specifies the interest calculation method in the final coupon period. Default: \code{TRUE}.
#' @param Calc.Method If 1, discount powers are computed with the same DCC as accrued interest.
#' If 0, discount powers are computed with DCC=2. Default: 1.
#' @param AnnivDatesOutput A list containing the output of the function AnnivDates. Default: \code{NA}.
#'
#' @return
#' \describe{
#' \item{CP}{The bond's clean price.}
#' \item{AccrInt}{The amount of accrued interest.}
#' \item{DP}{The bond's dirty price.}
#' \item{ytm.p.a.}{Annualized yield to maturity.}
#' \item{ModDUR.inYears}{Modified duration in years.}
#' \item{MacDUR.inYears}{MacAulay duration in years.}
#' \item{Conv.inYears}{Convexity in years.}
#' \item{ModDUR.inPeriods}{Modified duration in periods.}
#' \item{MacDUR.inPeriods}{MacAulay duration in periods.}
#' \item{Conv.inPeriods}{Convexity in periods.}
#' \item{tau}{Relative Position of the settlement date in regular periods.}
#' }
#'
#' @references
#' \enumerate{
#' \item{Djatschenko, Wadim, The Nitty Gritty of Bond Valuation: A Generalized Methodology for Fixed Coupon Bond Analysis Allowing for Irregular Periods and Various Day Count Conventions (November 5, 2018). Available at SSRN: https://ssrn.com/abstract=3205167.}
#' }
#'
#' @examples
#' data(PanelSomeBonds2016)
#' randombond<-sample(c(1:length(which(!(duplicated(PanelSomeBonds2016$ID.No))))),1)
#' df.randombond<-PanelSomeBonds2016[which(PanelSomeBonds2016$ID.No==randombond),]
#'
#' PreAnalysis.randombond<-suppressWarnings(AnnivDates(
#' unlist(df.randombond[
#' 1,c('Issue.Date','Mat.Date','CpY.Input','FIPD.Input','LIPD.Input',
#' 'FIAD.Input','RV.Input','Coup.Input','DCC.Input','EOM.Input')],
#' use.names=FALSE)))
#'
#' system.time(
#' for (i in c(1:nrow(df.randombond))) {
#' BondVal.Price.Output<-suppressWarnings(BondVal.Price(
#' unlist(
#' df.randombond[
#' i,c('YtM.Input','TradeDate','Issue.Date','Mat.Date','CpY.Input',
#' 'FIPD.Input','LIPD.Input','FIAD.Input','RV.Input','Coup.Input',
#' 'DCC.Input','EOM.Input')],use.names=FALSE),
#' AnnivDatesOutput=PreAnalysis.randombond))
#' df.randombond$CP.Out[i]<-BondVal.Price.Output$CP
#' }
#' )
#' plot(seq(1,nrow(df.randombond),by=1),df.randombond$CP.Out,"l")
#'
#' @export
#'
BondVal.Price<-function(YtM=as.numeric(NA),SETT=as.Date(NA),Em=as.Date(NA),Mat=as.Date(NA),CpY=as.numeric(NA),FIPD=as.Date(NA),LIPD=as.Date(NA),FIAD=as.Date(NA),RV=as.numeric(NA),Coup=as.numeric(NA),DCC=as.numeric(NA),EOM=as.numeric(NA),DateOrigin=as.Date("1970-01-01"),InputCheck=1,FindEOM=FALSE,RegCF.equal=0,SimpleLastPeriod=TRUE,Calc.Method=1,AnnivDatesOutput=as.list(NA)) {
if (length(YtM)>1) {
arglist<-YtM
argnames<-c("YtM","SETT","Em","Mat","CpY","FIPD","LIPD","FIAD","RV","Coup","DCC","EOM","DateOrigin","InputCheck","FindEOM","RegCF.equal","SimpleLastPeriod","Calc.Method")
for (i in c(1:length(arglist))) {
assign(argnames[i],arglist[i])
}
}
if (InputCheck==1) {
CheckedInput<-InputFormatCheck(YtM=YtM,SETT=SETT,Em=Em,Mat=Mat,CpY=CpY,FIPD=FIPD,LIPD=LIPD,FIAD=FIAD,RV=RV,Coup=Coup,DCC=DCC,EOM=EOM,DateOrigin=DateOrigin)
YtM<-CheckedInput$YtM
SETT<-CheckedInput$SETT
Em<-CheckedInput$Em
Mat<-CheckedInput$Mat
CpY<-CheckedInput$CpY
FIPD<-CheckedInput$FIPD
LIPD<-CheckedInput$LIPD
FIAD<-CheckedInput$FIAD
RV<-CheckedInput$RV
Coup<-CheckedInput$Coup
DCC<-CheckedInput$DCC
EOM<-CheckedInput$EOM
DateOrigin<-CheckedInput$DateOrigin
}
DP<-as.numeric(NA)
CP<-as.numeric(NA)
n<-as.numeric(NA)
k<-as.numeric(NA)
CN_tau<-as.numeric(NA)
tau<-as.numeric(NA)
w<-as.numeric(NA)
eta<-as.numeric(NA)
z<-as.numeric(NA)
AccrInt<-as.numeric(NA)
ModDUR.inYears<-as.numeric(NA)
MacDUR.inYears<-as.numeric(NA)
Conv.inYears<-as.numeric(NA)
ModDUR.inPeriods<-as.numeric(NA)
MacDUR.inPeriods<-as.numeric(NA)
Conv.inPeriods<-as.numeric(NA)
CF_final<-as.numeric(NA)
CF.remain<-as.numeric(NA)
DiscPowerVector<-as.numeric(NA)
PriceEqn<-as.numeric(NA)
if ((missing(YtM))|(is.na(YtM))) {
YtM<-as.numeric(NA)
warning("Yield to maturity (YtM) is missing or NA. NA created!")
} else {
if ((missing(SETT))|(is.na(SETT))) {
SETT<-as.Date(NA)
warning("Settlement date (SETT) is missing or NA. NA created!")
} else {
if ((SETT<Em)|(Mat<=SETT)) {
warning("Settlement date (SETT) is outside bond's lifespan. NA created!")
} else {
if (Calc.Method==0) {
RegCF.equal<-1
BondAnalysis<-suppressWarnings(AnnivDates(Em=Em,Mat=Mat,CpY=CpY,FIPD=FIPD,LIPD=LIPD,FIAD=FIAD,RV=RV,Coup=Coup,DCC=DCC,EOM=EOM,DateOrigin=DateOrigin,InputCheck=0,FindEOM=FindEOM,RegCF.equal=RegCF.equal))
} else {
if (all(is.na(AnnivDatesOutput))) {
BondAnalysis<-suppressWarnings(AnnivDates(Em=Em,Mat=Mat,CpY=CpY,FIPD=FIPD,LIPD=LIPD,FIAD=FIAD,RV=RV,Coup=Coup,DCC=DCC,EOM=EOM,DateOrigin=DateOrigin,InputCheck=0,FindEOM=FindEOM,RegCF.equal=RegCF.equal))
} else {
BondAnalysis<-AnnivDatesOutput
}
}
CpY<-BondAnalysis$Traits$CpY
RV<-BondAnalysis$Traits$Par
RealDates<-na.omit(BondAnalysis$DateVectors$RealDates)
if ((SETT<RealDates[1])|(SETT>=RealDates[length(RealDates)])) {
warning("Settlement date (SETT) is not between issue date (Em) and maturity date (Mat). NA created!")
} else {
if (is.na(BondAnalysis$Traits$FIPD)) {
FIPD<-BondAnalysis$Traits$est_FIPD
} else {
FIPD<-BondAnalysis$Traits$FIPD
}
if (is.na(BondAnalysis$Traits$LIPD)) {
LIPD<-BondAnalysis$Traits$est_LIPD
} else {
LIPD<-BondAnalysis$Traits$LIPD
}
DP.Output<-DP(RV,SETT,Em,Mat,CpY,FIPD,LIPD,FIAD,RV,Coup,DCC,EOM,DateOrigin,InputCheck=0,FindEOM,AnnivDatesOutput=BondAnalysis)
if (BondAnalysis$Warnings$ZeroFlag==1) {
Coup<-as.numeric(0)
CpY<-as.numeric(1)
}
AccrInt<-DP.Output[[2]]$Accrued_Interest
CF.values<-na.omit(BondAnalysis$PaySched$CoupPayments)
CF.dates<-na.omit(BondAnalysis$PaySched$CoupDates)
CF_List<-list(CF.values,CF.dates)
Use.ClosedForm<-as.numeric(0)
if (length(CF.values)>2) {
if (length(which(!duplicated(CF.values[-c(1,length(CF.values))])==TRUE))==1) {
Use.ClosedForm<-as.numeric(1)
}
}
if (Calc.Method==0) {
DCC_Orig<-DCC
DCC<-2
BondAnalysis<-suppressWarnings(AnnivDates(Em=Em,Mat=Mat,CpY=CpY,FIPD=FIPD,LIPD=LIPD,FIAD=FIAD,RV=RV,Coup=Coup,DCC=DCC,EOM=EOM,DateOrigin=DateOrigin,InputCheck=0,FindEOM=FindEOM,RegCF.equal=RegCF.equal))
}
# loading AnnivDates and expanding by one value to each side
AD.set<-na.omit(BondAnalysis$DateVectors$AnnivDates)
Refer<-BondAnalysis$Traits$Refer
AtomVector_Refer<-as.numeric(unlist(strsplit(as.character(Refer),split = "-")))
Atom1Refer<-AtomVector_Refer[1]
Atom2Refer<-AtomVector_Refer[2]
Atom3Refer<-AtomVector_Refer[3]
# creating the anniversary date preceding AD1
AtomVector_AD1<-as.numeric(unlist(strsplit(as.character(AD.set[1]),split = "-")))
Atom1AD1<-AtomVector_AD1[1]
Atom2AD1<-AtomVector_AD1[2]
Atom3AD1<-AtomVector_AD1[3]
PrevDate<-as.numeric(CppPrevDate(c(Atom1AD1,Atom2AD1,Atom3AD1,Atom1AD1,Atom2AD1,Atom3AD1,Atom1Refer,Atom2Refer,Atom3Refer,CpY,EOM)))
PrevDate<-as.Date(paste(PrevDate[1],PrevDate[2],PrevDate[3],sep="-"))
AD.set<-c(PrevDate,AD.set)
AD.set<-sort(na.omit(AD.set[!duplicated(AD.set)]))
# creating the anniversary date succeeding ADfin
AtomVector_ADfin<-as.numeric(unlist(strsplit(as.character(AD.set[length(AD.set)]),split = "-")))
Atom1ADfin<-AtomVector_ADfin[1]
Atom2ADfin<-AtomVector_ADfin[2]
Atom3ADfin<-AtomVector_ADfin[3]
SuccDate<-as.numeric(CppSuccDate(c(Atom1ADfin,Atom2ADfin,Atom3ADfin,Atom1ADfin,Atom2ADfin,Atom3ADfin,Atom1Refer,Atom2Refer,Atom3Refer,CpY,EOM)))
SuccDate<-as.Date(paste(SuccDate[1],SuccDate[2],SuccDate[3],sep="-"))
AD.set<-c(AD.set,SuccDate)
AD.set<-sort(na.omit(AD.set[!duplicated(AD.set)]))
AD.indexes<-na.omit(BondAnalysis$DateVectors$AD_indexes)
AD.indexes<-c((AD.indexes[1]-1),AD.indexes,(AD.indexes[length(AD.indexes)]+1))
SD.set<-na.omit(BondAnalysis$DateVectors$RealDates)
SD.indexes<-na.omit(BondAnalysis$DateVectors$RD_indexes)
AD_List<-list(AD.set,AD.indexes)
SD_List<-list(SD.set,SD.indexes)
### calculating tau
AtomVector_Mat<-as.numeric(unlist(strsplit(as.character(Mat),split = "-")))
Atom1Mat<-AtomVector_Mat[1]
Atom2Mat<-AtomVector_Mat[2]
Atom3Mat<-AtomVector_Mat[3]
AtomVector_PCD.SETT<-as.numeric(unlist(strsplit(as.character(PCD(SETT,AD.set)),split = "-")))
Atom1_PCD.SETT<-AtomVector_PCD.SETT[1]
Atom2_PCD.SETT<-AtomVector_PCD.SETT[2]
Atom3_PCD.SETT<-AtomVector_PCD.SETT[3]
AtomVector_SETT<-as.numeric(unlist(strsplit(as.character(SETT),split = "-")))
Atom1_SETT<-AtomVector_SETT[1]
Atom2_SETT<-AtomVector_SETT[2]
Atom3_SETT<-AtomVector_SETT[3]
AtomVector_NCD.SETT<-as.numeric(unlist(strsplit(as.character(NCD(SETT,AD.set)),split = "-")))
Atom1_NCD.SETT<-AtomVector_NCD.SETT[1]
Atom2_NCD.SETT<-AtomVector_NCD.SETT[2]
Atom3_NCD.SETT<-AtomVector_NCD.SETT[3]
AtomVector_NCD.NCD.SETT<-as.numeric(unlist(strsplit(as.character(NCD(NCD(SETT,AD.set),AD.set)),split = "-")))
Atom1_NCD.NCD.SETT<-AtomVector_NCD.NCD.SETT[1]
Atom2_NCD.NCD.SETT<-AtomVector_NCD.NCD.SETT[2]
Atom3_NCD.NCD.SETT<-AtomVector_NCD.NCD.SETT[3]
if (is.element(DCC,c(1,3,5,6,8,10,11,12,15))) {
tau_Num<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_SETT,Atom2_SETT,Atom3_SETT))[2]
tau_Den<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT))[2]
}
if (DCC==16) {
NonBus.PCD.SETT<-length(which((NonBusDays.Brazil$Date>=PCD(SETT,AD.set))&(NonBusDays.Brazil$Date<SETT)))
NonBus.PCD.NCD<-length(which((NonBusDays.Brazil$Date>=PCD(SETT,AD.set))&(NonBusDays.Brazil$Date<NCD(SETT,AD.set))))
tau_Num<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_SETT,Atom2_SETT,Atom3_SETT,NonBus.PCD.SETT))[2]
tau_Den<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,NonBus.PCD.NCD))[2]
}
if (DCC==2|DCC==14) {
OrigDCC<-DCC
DCC<-2
tau_Num<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,
Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_SETT,Atom2_SETT,Atom3_SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,
AD_List[[2]][which(AD_List[[1]]==PCD(SETT,AD.set))],
AD_List[[2]][which(AD_List[[1]]==NCD(PCD(SETT,AD.set),AD.set))],
CpY))[2]
tau_Den<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,
Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,Atom1_NCD.NCD.SETT,Atom2_NCD.NCD.SETT,Atom3_NCD.NCD.SETT,
AD_List[[2]][which(AD_List[[1]]==PCD(NCD(SETT,AD.set),AD.set))],
AD_List[[2]][which(AD_List[[1]]==NCD(PCD(SETT,AD.set),AD.set))],
CpY))[2]
DCC<-OrigDCC
}
if (DCC==4) {
tau_Num<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_SETT,Atom2_SETT,Atom3_SETT,Atom1_NCD.SETT,CpY))[2]
tau_Den<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,Atom1_NCD.NCD.SETT,CpY))[2]
}
if (DCC==7) {
tau_Num<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_SETT,Atom2_SETT,Atom3_SETT,Atom1Mat,Atom2Mat,Atom3Mat))[2]
tau_Den<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,Atom1Mat,Atom2Mat,Atom3Mat))[2]
}
if (is.element(DCC,c(9,13))) {
tau_Num<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_SETT,Atom2_SETT,Atom3_SETT,EOM))[2]
tau_Den<-DIST(c(DCC,Atom1_PCD.SETT,Atom2_PCD.SETT,Atom3_PCD.SETT,Atom1_NCD.SETT,Atom2_NCD.SETT,Atom3_NCD.SETT,EOM))[2]
}
tau<-tau_Num/tau_Den+AD_List[[2]][which(AD_List[[1]]==PCD(SETT,AD.set))]
n<-SD.indexes[length(SD.indexes)-1]
l<-BondAnalysis$Traits$LCPLength
if ((!(is.na(LIPD)))&(SETT<LIPD)) {
k<-SD_List[[2]][which(SD_List[[1]]==NCD(SETT,SD.set))]
w<-k-tau
eta<-n-k
z<-l
CN_tau<-CF_List[[1]][which(CF_List[[2]]==NCD(SETT,SD.set))]
} else {
k<-n
w<-SD_List[[2]][which(SD_List[[1]]==NCD(SETT,SD.set))]-tau
eta<-0
z<-0
CN_tau<-0
}
###################>>>>>> <<<<<<<##########################################################
##############>>>>>> calculation of CP, ModDUR, MacDUR and Conv <<<<<<<#####################################################
###################>>>>>> <<<<<<<##########################################################
CF_final<-CF.values[length(CF.values)]+RV
if ((z==0)&(SimpleLastPeriod==TRUE)) { # simple interest
a<-1+YtM*w/(100*CpY)
DP<-CF_final/a
CP<-DP-AccrInt
ModDUR.inYears<-(-1)*(1/DP)*(-1)*CF_final*(a^(-2))*(w/CpY)
MacDUR.inYears<-ModDUR.inYears*a
Conv.inYears<-0.5*(1/DP)*2*CF_final*(a^(-3))*(w/CpY)^2
ModDUR.inPeriods<-ModDUR.inYears*CpY
MacDUR.inPeriods<-MacDUR.inYears*CpY
Conv.inPeriods<-Conv.inYears*(CpY^2)
} else {
a<-1+YtM/(100*CpY)
# if (round(a,8)==1) {
# CF.remain<-CF_List[[1]][which(CF_List[[2]]>SETT)]
# CF.remain<-c(CF.remain[-length(CF.remain)],CF.remain[length(CF.remain)]+RV)
# DP<-sum(CF.remain)
# CP<-DP-AccrInt
# } else {
#
# }
if ((Use.ClosedForm==1)&(!(round(a,8)==1))) {
CF<-CF.values[2]
DP<-(a^(-w))*(CN_tau+CF*(((a^eta)-1)/((a^eta)*(a-1)))+CF_final/(a^(eta+z)))
CP<-DP-AccrInt
ModDUR.inYears<-ModDUR(a,c(1,CN_tau,CF,CF_final,w,eta,z,CpY,DP))
# ModDUR.inYears<-(-1)*(1/DP)*dm_MyPriceEqn(a,c(1,CN_tau,CF,CF_final,w,eta,z,CpY))
MacDUR.inYears<-ModDUR.inYears*a
Conv.inYears<-CONV(a,c(2,CN_tau,CF,CF_final,w,eta,z,CpY,DP))
# Conv.inYears<-0.5*(1/DP)*dm_MyPriceEqn(a,c(2,CN_tau,CF,CF_final,w,eta,z,CpY))
ModDUR.inPeriods<-ModDUR.inYears*CpY
MacDUR.inPeriods<-MacDUR.inYears*CpY
Conv.inPeriods<-Conv.inYears*(CpY^2)
} else {
if (z>0) {
DiscPowerVector<-c((seq(0,eta,by=1)+w),(w+eta+z))
} else {
DiscPowerVector<-w
}
CF.remain<-CF_List[[1]][which(CF_List[[2]]>SETT)]
CF.remain<-c(CF.remain[-length(CF.remain)],CF.remain[length(CF.remain)]+RV)
# creating the price equation
summands<-gsub(" ","",paste(CF.remain,"/(a^",DiscPowerVector,")"))
PriceEqn<-paste(summands,collapse="+")
PriceFunction.Standard<-function(a) {
out<-eval(parse(text=PriceEqn))
return(out)
}
# creating the first derivative of the price function
d_PowerVector<-DiscPowerVector+1
d_summands<-gsub(" ","",paste("(-1)*(",CF.remain,"*",DiscPowerVector,"/(a^",d_PowerVector,"))"))
d_PriceEqn<-paste(d_summands,collapse="+")
d_PriceFunction.Standard<-function(a) {
out<-eval(parse(text=d_PriceEqn))
return(out)
}
DP<-PriceFunction.Standard(a)
CP<-DP-AccrInt
# calculating the Modified Duration and the MacAulay Duration
ModDUR.inPeriods<-(-1)*(1/DP)*d_PriceFunction.Standard(a)
MacDUR.inPeriods<-ModDUR.inPeriods*a
ModDUR.inYears<-ModDUR.inPeriods/CpY
MacDUR.inYears<-MacDUR.inPeriods/CpY
# calculating the Convexity
d2_PowerVector<-d_PowerVector+1
d2_summands<-gsub(" ","",paste("(",CF.remain,"*",DiscPowerVector,"*",d_PowerVector,")/(a^",d2_PowerVector,")"))
Added.d2_summands<-paste(d2_summands,collapse="+")
d2_PriceFunction.Standard <- function(a) {
out<-eval(parse(text=Added.d2_summands))
return(out)
}
Conv.inPeriods<-(1/DP)*0.5*d2_PriceFunction.Standard(a)
Conv.inYears<-Conv.inPeriods/(CpY^2)
}
}
}
}
}
}
# out<-list(tau=tau,n=n,k=k,w=w,eta=eta,z=z,CN_tau=CN_tau,ytm.p.a.=YtM,DP=DP,CF_final=CF_final,
# ModDUR.inPeriods=ModDUR.inPeriods,MacDUR.inPeriods=MacDUR.inPeriods,Conv.inPeriods=Conv.inPeriods,
# ModDUR.inYears=ModDUR.inYears,MacDUR.inYears=MacDUR.inYears,Conv.inYears=Conv.inYears,FIPD=FIPD,
# LIPD=LIPD)
# out<-Added.d2_summands
out<-list(CP=CP,AccrInt=AccrInt,DP=DP,ytm.p.a.=YtM,ModDUR.inYears=ModDUR.inYears,MacDUR.inYears=MacDUR.inYears,
Conv.inYears=Conv.inYears,ModDUR.inPeriods=ModDUR.inPeriods,MacDUR.inPeriods=MacDUR.inPeriods,
Conv.inPeriods=Conv.inPeriods,tau=tau)
return(out)
}
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