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Finance[CleanPrice] - calculate the clean price of a bond

Calling Sequence

CleanPrice(bond, yield, compounding, opts)

Parameters

bond

-

fixed or floating rate bond data structure; bond

yield

-

non-negative constant; desired yield

compounding

-

Simple, Continuous, Compounded, or SimpleThenCompounded; the underlying compounding type

opts

-

equations of the form option = value where option is evaluationdate; specify options for the CleanPrice command

Description

• 

The CleanPrice command computes the clean price of a bond, given its yield. Clean price does not include any accrued interest that has accumulated since the last coupon payment.

• 

The parameter bond is either a fixed coupon bond or floating rate bond. The parameter yield is the desired yield.

Examples

withFinance:

SetEvaluationDateNovember 25, 2006:

EvaluationDate

November 25, 2006

(1)

Settingsdaycounter=Historical,settlementdays=0,businessdayconvention=Unadjusted,compounding=Continuous

daycounter=Historical,settlementdays=0,businessdayconvention=Unadjusted,compounding=Continuous

(2)

Consider a zero-coupon bond with a face value of 100 maturing in one year.

bond1:=ZeroCouponBond100,5,Years:

price1:=CleanPricebond1,0.05,Compounded

price1:=78.35261665

(3)

100DiscountFactor0.05,5,compounding=Annual

78.35261665

(4)

10011.055

78.35261665

(5)

yield1:=YieldFromCleanPricebond1,price1

yield1:=0.04879016417

(6)

EquivalentRateyield1,Continuous,Annual

0.05000000000

(7)

yield1:=YieldFromCleanPricebond1,price1,Compounded

yield1:=0.05000000006

(8)

Consider a 3-year bond with a face value of 100 that pays a fixed coupon of 3 percent issued on March 15, 2005.

Settingsdaycounter=Thirty360European:

Settingsdaycounter

Thirty360European

(9)

principal2:=100:

coupon2:=0.03:

rate2:=0.05:

bond2:=FixedCouponBondprincipal2,3,Years,coupon2,issuedate=March 17, 2005:

Calculate the bond's clean price given its yield and vice-versa.

yield2:=YieldFromCleanPricebond2,100,Compounded

yield2:=0.02992505925

(10)

cleanprice2:=CleanPricebond2,yield2,Compounded

cleanprice2:=100.0000000

(11)

YieldFromCleanPricebond2,cleanprice2

0.02948604163

(12)

CleanPricebond2,rate2

97.35137029

(13)

dirtyprice2:=DirtyPricebond2,rate2

dirtyprice2:=99.41803696

(14)

YieldFromDirtyPricebond2,dirtyprice2

0.05000000002

(15)

Consider the same bond but with semi-annual coupons.

bond3:=FixedCouponBondprincipal2,3,Years,coupon2,issuedate=March 17, 2005,frequency=Semiannual:

Calculate the bond's clean price given its yield and vice-versa.

yield3:=YieldFromCleanPricebond3,100,Compounded

yield3:=0.02997946101

(16)

cleanprice3:=CleanPricebond3,yield3,Compounded

cleanprice3:=100.0000000

(17)

YieldFromCleanPricebond3,cleanprice3

0.02975698958

(18)

CleanPricebond3,rate2

97.41008628

(19)

dirtyprice3:=DirtyPricebond3,rate2

dirtyprice3:=97.97675295

(20)

YieldFromDirtyPricebond3,dirtyprice3

0.05000000002

(21)

Note that since the bond has semi-annual coupons, the Compounded yield is based on semi-annual compounding.

dirtyprice3:=DirtyPricebond3,rate2,Compounded

dirtyprice3:=98.05440635

(22)

cashflows3:=CashFlowsbond3

cashflows3:=1.500000000 on 'March 17, 2007',1.500000000 on 'September 17, 2007',1.500000000 on 'March 17, 2008',100. on 'March 17, 2008'

(23)

addtamountDiscountFactorrate2,tdate,compounding=Semiannual,t∈cashflows3

98.05440635

(24)

See Also

Finance[AccruedInterest], Finance[DayCounter], Finance[DirtyPrice], Finance[EvaluationDate], Finance[FixedCouponBond], Finance[FloatingRateBond], Finance[FormatDate], Finance[ParseDate], Finance[Settings], Finance[YearFraction], Finance[YieldFromCleanPrice], Finance[YieldFromDirtyPrice], Finance[ZeroCouponBond]


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