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Finance

  

Duration

  

calculate the duration of a set of cash flows or bonds

 

Calling Sequence

Parameters

Options

Description

Examples

Compatibility

Calling Sequence

Duration(cashflows, rate, opts)

Duration(bond, rate, opts)

Parameters

cashflows

-

cash flow data structure or a list of cash flow data structures; cash flows

bond

-

fixed- or floating-rate bond data structure; bond

rate

-

non-negative real number; interest rate

opts

-

equations of the form option = value where option is one of evaluation, compounding, or daycounter; specify options for the Duration command

Options

• 

compounding = Simple, Continuous, Annual, Semiannual, EveryFourthMonth, Quarterly, Bimonthly, Monthly, SimpleThenAnnual, SimpleThenSemiannual, SimpleThenEveryFourthMonth, SimpleThenQuarterly, SimpleThenBimonthly, or SimpleThenMonthly -- This option specifies the compounding type for the given interest rate.

• 

daycounter = Actual360, Actual365Fixed, AFB, Bond, Euro, Historical, ISDA, ISMA, OneDay, Simple, Thirty360BondBasis, Thirty360EuroBondBasis, Thirty360European, Thirty360Italian, Thirty360USA, or a day counter data structure created using the DayCounter constructor -- This option provides a day counter that will be used to represent the period between two dates as a fraction of the year. The default day count convention can be set using the Settings command.

• 

evaluationdate =  a string containing a date specification in a format recognized by ParseDate or a date data structure -- This option specifies the evaluation date. This is set to the global evaluation date by default (see EvaluationDate).

Description

• 

The Duration command calculates the duration of a set of cash flows or a portfolio of bonds.

• 

For a set of cash flows Ct the simple duration is defined as

ttCtPttCtPt

where Pt is the discount at time t implied by the given interest rate. There are at least two ways to calculate Pt. One can either use a yield term structure or an internal rate of return of the set of cash flows. In the latter case one would obtain the Macaulay duration.

• 

A bond's duration is defined in a similar way. It can also be interpreted as the weighted first derivative of the price:

ⅆⅆrBrBr

• 

Duration is useful as a measure of sensitivity of a bond's or cash flows' price to interest rate movements.

• 

The parameter cashflows is a cash flow data structure or a list of cash flow data structures.

• 

The parameter bond must be a fixed- or floating-rate bond data structure.

Examples

withFinance:

SetEvaluationDateJanuary 1, 2005:

paymentdateJanuary 1, 2007

paymentdate:=January 1, 2007

(1)

cashflow1seqSimpleCashFlow100,AdvanceDatepaymentdate,i,Years,i=1..10

cashflow1:=100. on January 1, 2008,100. on January 1, 2009,100. on January 1, 2010,100. on January 1, 2011,100. on January 1, 2012,100. on January 1, 2013,100. on January 1, 2014,100. on January 1, 2015,100. on January 1, 2016,100. on January 1, 2017

(2)

Durationcashflow1,0.03,evaluationdate=January 1, 2005

7.252874161

(3)

Durationcashflow1,0.03,evaluationdate=January 1, 2004

8.252874161

(4)

Here is another example.

nominalamt100

nominalamt:=100

(5)

rate0.05

rate:=0.05

(6)

startdateJanuary 1, 2006

startdate:=January 1, 2006

(7)

cashflow2seqFixedRateCouponnominalamt,rate,startdate,AdvanceDatestartdate,i,Years,i=1..10

cashflow2:=5. on January 1, 2007,10. on January 1, 2008,15. on January 1, 2009,20. on January 1, 2010,25. on January 1, 2011,30. on January 1, 2012,35. on January 1, 2013,40. on January 1, 2014,45. on January 1, 2015,50. on January 1, 2016

(8)

Compute the value of this cash flow on January 1, 2005.

Durationcashflow2,0.03,evaluationdate=January 1, 2005

7.816330091

(9)

Compute the Macaulay duration for the previous cash flow.

irrInternalRateOfReturncashflow2,15

irr:=0.4458188048

(10)

Durationcashflow2,irr

5.076090247

(11)

Here is an example using bonds.

bondFixedCouponBond100,5,Years,0.05

bond:=moduleend module

(12)

cflowsCashFlowsbond

cflows:=5. on 'January 1, 2006',5. on 'January 1, 2007',5. on 'January 1, 2008',5. on 'January 1, 2009',5. on 'January 1, 2010',100. on 'January 1, 2010'

(13)

Durationbond,0.03,evaluationdate=January 5, 2000

9.556636250

(14)

Durationcflows,0.03,evaluationdate=January 5, 2000

9.556636250

(15)

Compatibility

• 

The Finance[Duration] command was introduced in Maple 15.

• 

For more information on Maple 15 changes, see Updates in Maple 15.

See Also

Finance[CompoundFactor]

Finance[Convexity]

Finance[DiscountFactor]

Finance[FixedRateCoupon]

Finance[InArrearIndexedCoupon]

Finance[NetPresentValue]

Finance[ParCoupon]

Finance[SimpleCashFlow]

Finance[UpFrontIndexedCoupon]

Finance[ZeroCurve]

 


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