FixedRateBond: Fixed-Rate bond pricing

Description

The FixedRateBond function evaluates a fixed rate bond using discount curve, the yield or the clean price. More specificly, when a discount curve is provided the calculation is done by DiscountingBondEngine from QuantLib. The NPV, clean price, dirty price, accrued interest, yield, duration, actual settlement date and cash flows of the bond is returned. When a yield is provided instead, no engine is provided to the bond class and prices are computed from yield. In the latter case, NPV is set to NA. Same situation when the clean price is given instead of discount curve or yield. For more detail, see the source codes in QuantLib's file test-suite/bond.cpp.

The FixedRateBondPriceByYield function calculates the theoretical price of a fixed rate bond from its yield.

The FixedRateBondYield function calculates the theoretical yield of a fixed rate bond from its price.

Usage

"FixedRateBond"(bond, rates, schedule, calc=list(dayCounter='ActualActual.ISMA', compounding='Compounded', freq='Annual', durationType='Modified'), discountCurve = NULL, yield = NA, price = NA)
"FixedRateBondPriceByYield"( settlementDays=1, yield, faceAmount=100,  effectiveDate, maturityDate, period, calendar="UnitedStates/GovernmentBond",  rates, dayCounter=2, businessDayConvention=0, compound = 0, redemption=100,  issueDate)
"FixedRateBondYield"( settlementDays=1, price, faceAmount=100,  effectiveDate, maturityDate, period, calendar="UnitedStates/GovernmentBond",  rates, dayCounter=2, businessDayConvention=0,  compound = 0, redemption=100,  issueDate)

Arguments

bond

(Optional) bond parameters, a named list whose elements are:

settlementDays

(Optional) a double, settlement days.

Default value is 1.

faceAmount

(Optional) a double, face amount of the bond.

Default value is 100.

dayCounter

(Optional) a number or string,

day counter convention. Defaults to 'Thirty360'

issueDate

(Optional) a Date, the bond's issue date

Defaults to QuantLib default.

paymentConvention

(Optional) a number or string, the bond

payment convention.

Defaults to QuantLib default.

redemption

(Optional) a double, the redemption amount.

Defaults to QuantLib default (100).

paymentCalendar

(Optional) a string, the name of the calendar.

Defaults to QuantLib default.

exCouponPeriod

(Optional) a number, the number of days when

the coupon goes ex relative to the coupon date.

Defaults to QuantLib default.

exCouponCalendar

(Optional) a string, the name of the

ex-coupon calendar.

Defaults to QuantLib default.

exCouponConvention

(Optional) a number or string, the coupon

payment convention.

Defaults to QuantLib default.

exCouponEndOfMonth

(Optional) 1 or 0, use End of Month rule for

rates

a numeric vector, bond's coupon rates

schedule

(Optional) a named list, QuantLib's parameters of the bond's schedule.

effectiveDate

a Date, when the schedule becomes effective.

maturityDate

a Date, when the schedule matures.

period

(Optional) a number or string, the frequency of

the schedule. Default value is 'Semiannual'.

calendar

(Optional) a string, the calendar name.

Defaults to 'TARGET'

businessDayConvention

(Optional) a number or string, the

day convention to use.

Defaults to 'Following'.

terminationDateConvention

(Optional) a number or string, the

day convention to use for the terminal date.

Defaults to 'Following'.

dateGeneration

(Optional) a number or string, the

date generation rule.

Defaults to 'Backward'.

endOfMonth

(Optional) 1 or 0, use End of Month rule for

See example below.

calc

(Optional) a named list, QuantLib's parameters for calculations.

dayCounter

(Optional) a number or string, day counter

convention. Defaults to 'ActualActual.ISMA'

compounding

a string, what kind of compounding to use.

Defaults to 'Compounded'

freq

(Optional) a number or string, the frequency

to use. Default value is 'Annual'.

durationType

(Optional) a number or string, the type of

duration to calculate. Defaults to 'Simple'

accuracy

(Optional) a number, the accuracy required.

Defaults to 1.0e-8.

maxEvaluations

(Optional) a number, max number of iterations.

discountCurve

Can be one of the following:

a DiscountCurve

a object of DiscountCurve class

For more detail, see example or

the discountCurve function

A 2 items list

specifies a flat curve in two

values "todayDate" and "rate"

A 3 items list

specifies three values to construct a

DiscountCurve object, "params" ,

"tsQuotes", "times".

For more detail, see example or

yield

yield of the bond

price

clean price of the bond

settlementDays

an integer, 1 for T+1, 2 for T+2, etc...

effectiveDate

bond's effective date

maturityDate

bond's maturity date

period

frequency of events,0=NoFrequency, 1=Once, 2=Annual, 3=Semiannual, 4=EveryFourthMonth, 5=Quarterly, 6=Bimonthly ,7=Monthly ,8=EveryFourthWeek,9=Biweekly, 10=Weekly, 11=Daily. For more information, see QuantLib's Frequency class

calendar

Business Calendar. Either us or uk

faceAmount

face amount of the bond

businessDayConvention

convention used to adjust a date in case it is not a valid business day. See quantlib for more detail. 0 = Following, 1 = ModifiedFollowing, 2 = Preceding, 3 = ModifiedPreceding, other = Unadjusted

dayCounter

day count convention. 0 = Actual360(), 1 = Actual365Fixed(), 2 = ActualActual(), 3 = Business252(), 4 = OneDayCounter(), 5 = SimpleDayCounter(), all other = Thirty360(). For more information, see QuantLib's DayCounter class

compound

compounding type. 0=Simple, 1=Compounded, 2=Continuous, all other=SimpleThenCompounded. See QuantLib's Compound class

redemption

redemption when the bond expires

issueDate

date the bond is issued

Value

The FixedRateBond function returns an object of class FixedRateBond (which inherits from class Bond). It contains a list with the following components:The FixedRateBondPriceByYield function returns an object of class FixedRateBondPriceByYield (which inherits from class Bond). It contains a list with the following components:The FixedRateBondYield function returns an object of class FixedRateBondYield (which inherits from class Bond). It contains a list with the following components:

Details

A discount curve is built to calculate the bond value.

Please see any decent Finance textbook for background reading, and the QuantLib documentation for details on the QuantLib implementation.

References

http://quantlib.org for details on QuantLib.

Examples

Run this code

#Simple call with a flat curve
bond <- list(settlementDays=1,
             issueDate=as.Date("2004-11-30"),
             faceAmount=100,
             accrualDayCounter='Thirty360',
             paymentConvention='Unadjusted')
schedule <- list(effectiveDate=as.Date("2004-11-30"),
                 maturityDate=as.Date("2008-11-30"),
                 period='Semiannual',
                 calendar='UnitedStates/GovernmentBond',
                 businessDayConvention='Unadjusted',
                 terminationDateConvention='Unadjusted',
                 dateGeneration='Forward',
                 endOfMonth=1)
calc=list(dayCounter='Actual360',
          compounding='Compounded',
          freq='Annual',
          durationType='Modified')
coupon.rate <- c(0.02875)
                       
params <- list(tradeDate=as.Date('2002-2-15'),
               settleDate=as.Date('2002-2-19'),
               dt=.25,
               interpWhat="discount",
               interpHow="loglinear")
setEvaluationDate(as.Date("2004-11-22"))

discountCurve.flat <- DiscountCurve(params, list(flat=0.05))
FixedRateBond(bond,
              coupon.rate,
              schedule,
              calc,
              discountCurve=discountCurve.flat)


#Same bond with a discount curve constructed from market quotes
tsQuotes <- list(d1w  =0.0382,
                 d1m  =0.0372,
                 fut1=96.2875,
                 fut2=96.7875,
                 fut3=96.9875,
                 fut4=96.6875,
                 fut5=96.4875,
                 fut6=96.3875,
                 fut7=96.2875,
                 fut8=96.0875,
                 s3y  =0.0398,
                 s5y  =0.0443,
                 s10y =0.05165,
                 s15y =0.055175)
tsQuotes <- list("flat" = 0.02)		## While discount curve code is buggy

discountCurve <- DiscountCurve(params, tsQuotes)
FixedRateBond(bond,
              coupon.rate,
              schedule,
              calc,
              discountCurve=discountCurve)

#Same bond calculated from yield rather than from the discount curve
yield <- 0.02
FixedRateBond(bond,
              coupon.rate,
              schedule,
              calc,
              yield=yield)


#same example with clean price
price <- 103.31
FixedRateBond(bond,
              coupon.rate,
              schedule,
              calc,
              price = price)

#example with default calc parameter
FixedRateBond(bond,
              coupon.rate,
              schedule,
              discountCurve=discountCurve)
              
#example with default calc and schedule parameters
schedule <- list(effectiveDate=as.Date("2004-11-30"),
                 maturityDate=as.Date("2008-11-30"))
FixedRateBond(bond,
              coupon.rate,
              schedule,
              discountCurve=discountCurve)

#example with default calc, schedule and bond parameters
FixedRateBond(,
              coupon.rate,
              schedule,
              discountCurve=discountCurve)

FixedRateBondPriceByYield(,0.0307, 100000, as.Date("2004-11-30"),
                          as.Date("2008-11-30"), 3, , c(0.02875),
                          , , , ,as.Date("2004-11-30"))

FixedRateBondYield(,90, 100000, as.Date("2004-11-30"), as.Date("2008-11-30"),
                   3, , c(0.02875), , , , ,as.Date("2004-11-30"))

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