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## bonds.R -- following what bonds.py does for the QuantLib bindings for Python
suppressMessages(library(QuantLib))
## global data
calendar <- TARGET()
settlementDate <- Date(18, "September", 2008)
settlementDate <- Calendar_adjust(calendar, settlementDate)
fixingDays <- 3
settlementDays <- 3
todaysDate <- Calendar_advance(calendar, settlementDate, -fixingDays, "Days")
invisible(Settings_instance()$setEvaluationDate(d=todaysDate))
cat('Today : ', todaysDate$`__str__`(), "\n")
cat('Settlement Date: ', settlementDate$`__str__`(), "\n")
## market quotes
## constructing bond yield curve
zcQuotes <- list(rates=c(0.0096, 0.0145, 0.0194),
tenor=c(Period(3, "Months"),
Period(6, "Months"),
Period(1, "Years")))
zcBondsDayCounter <- Actual365Fixed()
bondInstruments <- RateHelperVector()
for (i in 1:3) {
r <- zcQuotes[["rates"]][i]
tenor <- zcQuotes[["tenor"]][[i]]
drh <- DepositRateHelper(QuoteHandle(SimpleQuote(r)),
tenor,
fixingDays,
calendar,
"ModifiedFollowing",
TRUE,
zcBondsDayCounter)
RateHelperVector_push_back(bondInstruments, drh)
}
## setup bonds
redemption <- 100.0
numberOfBonds <- 5
bondQuotes <- list(list(Date(15,"March",2005),
Date(31,"August",2010),
0.02375, 100.390625),
list(Date(15,"June",2005),
Date(31,"August",2011),
0.04625, 106.21875),
list(Date(30,"June",2006),
Date(31,"August",2013),
0.03125, 100.59375),
list(Date(15,"November",2002),
Date(15,"August",2018),
0.04000, 101.6875),
list(Date(15,"May",1987),
Date (15,"May",2038),
0.04500, 102.140625)
)
# Definition of the rate helpers
for (i in 1:5) {
issueDate <- bondQuotes[[i]][[1]]
maturity <- bondQuotes[[i]][[2]]
couponRate <- bondQuotes[[i]][[3]]
marketQuote <- bondQuotes[[i]][[4]]
schedule <- Schedule(issueDate, maturity, Period("Semiannual"),
UnitedStates("GovernmentBond"),
"Unadjusted", "Unadjusted",
copyToR(DateGeneration(), "Backward"),
FALSE)
bh <- FixedRateBondHelper(QuoteHandle(SimpleQuote(marketQuote)),
settlementDays,
100.0,
schedule,
couponRate,
ActualActual("Bond"),
"Unadjusted",
redemption,
issueDate)
RateHelperVector_push_back(bondInstruments, bh)
}
termStructureDayCounter <- ActualActual("ISDA")
# not needed as defined in the interface file: tolerance = 1.0e-15
bondDiscountingTermStructure <- PiecewiseFlatForward(settlementDate,
bondInstruments,
termStructureDayCounter)
# Building of the Libor forecasting curve
# deposits
dQuotes <- list(list(0.043375, Period(1,"Weeks")),
list(0.031875, Period(1,"Months")),
list(0.0320375, Period(3,"Months")),
list(0.03385, Period(6,"Months")),
list(0.0338125, Period(9,"Months")),
list(0.0335125, Period(1,"Years")))
sQuotes <- list(list(0.0295, Period(2,"Years")),
list(0.0323, Period(3,"Years")),
list(0.0359, Period(5,"Years")),
list(0.0412, Period(10,"Years")),
list(0.0433, Period(15,"Years")))
## deposits
depositDayCounter <- Actual360()
depoSwapInstruments <- RateHelperVector()
for (i in 1:length(dQuotes)) {
rate <- dQuotes[[i]][[1]]
tenor <- dQuotes[[i]][[2]]
drh <- DepositRateHelper(QuoteHandle(SimpleQuote(rate)),
tenor, fixingDays,
calendar, "ModifiedFollowing",
TRUE, depositDayCounter)
RateHelperVector_push_back(depoSwapInstruments, drh)
}
## swaps
swFixedLegFrequency <- "Annual"
swFixedLegConvention <- "Unadjusted"
swFixedLegDayCounter <- Thirty360("European")
swFloatingLegIndex <- Euribor6M()
forwardStart <- Period(1,"Days")
for (i in 1:length(sQuotes)) {
rate <- sQuotes[[i]][[1]]
tenor <- sQuotes[[i]][[2]]
srh <- SwapRateHelper(QuoteHandle(SimpleQuote(rate)), tenor,
calendar, swFixedLegFrequency,
swFixedLegConvention, swFixedLegDayCounter,
swFloatingLegIndex, QuoteHandle(),forwardStart)
RateHelperVector_push_back(depoSwapInstruments, srh)
}
depoSwapTermStructure <- PiecewiseFlatForward(settlementDate, depoSwapInstruments,
termStructureDayCounter)
## Term structures that will be used for pricing:
## the one used for discounting cash flows
discountingTermStructure <- RelinkableYieldTermStructureHandle()
## the one used for forward rate forecasting
forecastingTermStructure <- RelinkableYieldTermStructureHandle()
########################################
## BONDS TO BE PRICED #
########################################
## common data
faceAmount <- 100
## pricing engine
bondEngine <- DiscountingBondEngine(discountingTermStructure)
## zero coupon bond
zeroCouponBond <- ZeroCouponBond(settlementDays,
UnitedStates("GovernmentBond"),
faceAmount,
Date(15,"August",2013),
"Following",
116.92,
Date(15,"August",2003))
invisible(Instrument_setPricingEngine(zeroCouponBond, bondEngine))
## fixed 4.5% US Treasury note
fixedBondSchedule <- Schedule(Date(15, "May", 2007),
Date(15, "May",2017), Period("Semiannual"),
UnitedStates("GovernmentBond"),
"Unadjusted", "Unadjusted",
copyToR(DateGeneration(), "Backward"), FALSE)
fixedRateBond <- FixedRateBond(settlementDays,
faceAmount,
fixedBondSchedule,
0.045,
ActualActual("Bond"),
"ModifiedFollowing",
100.0, Date(15, "May", 2007))
invisible(Instrument_setPricingEngine(fixedRateBond, bondEngine))
## Floating rate bond (3M USD Libor + 0.1%)
## Should and will be priced on another curve later...
liborTermStructure <- RelinkableYieldTermStructureHandle()
libor3m <- USDLibor(Period(3,"Months"),liborTermStructure)
invisible(Index_addFixing(libor3m, Date(17, "July", 2008), 0.0278625))
floatingBondSchedule <- Schedule(Date(21, "October", 2005),
Date(21, "October", 2010), Period("Quarterly"),
UnitedStates("NYSE"),
"Unadjusted", "Unadjusted",
copyToR(DateGeneration(), "Backward"), TRUE)
floatingRateBond <- FloatingRateBond(settlementDays,
faceAmount,
floatingBondSchedule,
libor3m,
Actual360(),
"ModifiedFollowing",
2,
1.0, # Gearings
0.001, # Spreads
numeric(0), #[], # Caps
numeric(0), #[], # Floors
TRUE, # Fixing in arrears
100.0,
Date(21, "October", 2005))
invisible(Instrument_setPricingEngine(floatingRateBond, bondEngine))
## coupon pricers
pricer <- BlackIborCouponPricer()
## optionlet volatilities
volatility <- 0.0
vol <- ConstantOptionletVolatility(settlementDays,
calendar,
"ModifiedFollowing",
volatility,
Actual365Fixed())
invisible(IborCouponPricer_setCapletVolatility(pricer, OptionletVolatilityStructureHandle(vol)))
invisible(setCouponPricer(Bond_cashflows(floatingRateBond), pricer))
## Yield curve bootstrapping
invisible(RelinkableYieldTermStructureHandle_linkTo(forecastingTermStructure, depoSwapTermStructure))
invisible(RelinkableYieldTermStructureHandle_linkTo(discountingTermStructure, bondDiscountingTermStructure))
## We are using the depo & swap curve to estimate the future Libor rates
invisible(RelinkableYieldTermStructureHandle_linkTo(liborTermStructure, depoSwapTermStructure))
##
df <- data.frame(zeroCoupon=c(Instrument_NPV(zeroCouponBond),
Bond_cleanPrice(zeroCouponBond),
Bond_dirtyPrice(zeroCouponBond),
Bond_accruedAmount(zeroCouponBond),
NA,
NA,
100*Bond_yield(zeroCouponBond, Actual360(), "Compounded", "Annual")),
fixedRate=c(Instrument_NPV(fixedRateBond),
Bond_cleanPrice(fixedRateBond),
Bond_dirtyPrice(fixedRateBond),
Bond_accruedAmount(fixedRateBond),
100*Bond_previousCouponRate(fixedRateBond),
100*Bond_nextCouponRate(fixedRateBond),
100*Bond_yield(fixedRateBond, Actual360(), "Compounded", "Annual")),
floatingRate=c(Instrument_NPV(floatingRateBond),
Bond_cleanPrice(floatingRateBond),
Bond_dirtyPrice(floatingRateBond),
Bond_accruedAmount(floatingRateBond),
100*Bond_previousCouponRate(floatingRateBond),
100*Bond_nextCouponRate(floatingRateBond),
100*Bond_yield(floatingRateBond, Actual360(), "Compounded", "Annual")),
row.names=c("NPV", "Clean Price", "Dirty Price",
"Accrued Amount", "Previous Coupon", "Next Coupon", "Yield"))
cat("\nResults:\n")
print(df, digits=5)
# Other computations
cat("\nSample indirect computations (for the floating rate bond):\n")
yld <- Bond_yield(floatingRateBond, Actual360(), "Compounded", "Annual")
clnPrc <- Bond_cleanPrice(floatingRateBond, yld, Actual360(), "Compounded", "Annual", settlementDate)
cat("Yield to Clean Price: ", clnPrc, "\n")
yld <- Bond_yield(floatingRateBond, BondPrice(clnPrc, BondPrice_Clean_get()), Actual360(), "Compounded", "Annual",settlementDate)
cat("Clean Price to Yield: ", yld, "\n")
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