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).

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

For a set of cash flows $C\left(t\right)$ the simple duration is defined as

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

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.

$\mathrm{with}\left(\mathrm{Finance}\right)\:$

$\mathrm{SetEvaluationDate}\left(''January\; 1,\; 2005''\right)\:$

$\mathrm{paymentdate}≔''January\; 1,\; 2007''$

$\mathrm{paymentdate}≔''January\; 1,\; 2007''$

$\mathrm{cashflow1}≔\left[\mathrm{seq}\left(\mathrm{SimpleCashFlow}\left(100\,\mathrm{AdvanceDate}\left(\mathrm{paymentdate}\,i\,\mathrm{Years}\right)\right)\,i=1..10\right)\right]$

$\mathrm{cashflow1}≔\left[\mathrm{100.\; on\; January\; 1,\; 2008}\,\mathrm{100.\; on\; January\; 1,\; 2009}\,\mathrm{100.\; on\; January\; 1,\; 2010}\,\mathrm{100.\; on\; January\; 1,\; 2011}\,\mathrm{100.\; on\; January\; 1,\; 2012}\,\mathrm{100.\; on\; January\; 1,\; 2013}\,\mathrm{100.\; on\; January\; 1,\; 2014}\,\mathrm{100.\; on\; January\; 1,\; 2015}\,\mathrm{100.\; on\; January\; 1,\; 2016}\,\mathrm{100.\; on\; January\; 1,\; 2017}\right]$

$\mathrm{Duration}\left(\mathrm{cashflow1}\,0.03\,\mathrm{evaluationdate}=''January\; 1,\; 2005''\right)$

$7.252874161$

$\mathrm{Duration}\left(\mathrm{cashflow1}\,0.03\,\mathrm{evaluationdate}=''January\; 1,\; 2004''\right)$

$8.252874161$

$\mathrm{nominalamt}≔100$

$\mathrm{nominalamt}≔100$

$\mathrm{rate}≔0.05$

$\mathrm{rate}≔0.05$

$\mathrm{startdate}≔''January\; 1,\; 2006''$

$\mathrm{startdate}≔''January\; 1,\; 2006''$

$\mathrm{cashflow2}≔\left[\mathrm{seq}\left(\mathrm{FixedRateCoupon}\left(\mathrm{nominalamt}\,\mathrm{rate}\,\mathrm{startdate}\,\mathrm{AdvanceDate}\left(\mathrm{startdate}\,i\,\mathrm{Years}\right)\right)\,i=1..10\right)\right]$

$\mathrm{cashflow2}≔\left[\mathrm{5.\; on\; January\; 1,\; 2007}\,\mathrm{10.\; on\; January\; 1,\; 2008}\,\mathrm{15.\; on\; January\; 1,\; 2009}\,\mathrm{20.\; on\; January\; 1,\; 2010}\,\mathrm{25.\; on\; January\; 1,\; 2011}\,\mathrm{30.\; on\; January\; 1,\; 2012}\,\mathrm{35.\; on\; January\; 1,\; 2013}\,\mathrm{40.\; on\; January\; 1,\; 2014}\,\mathrm{45.\; on\; January\; 1,\; 2015}\,\mathrm{50.\; on\; January\; 1,\; 2016}\right]$

$\mathrm{Duration}\left(\mathrm{cashflow2}\,0.03\,\mathrm{evaluationdate}=''January\; 1,\; 2005''\right)$

$7.816330091$

$\mathrm{irr}≔\mathrm{InternalRateOfReturn}\left(\mathrm{cashflow2}\,15\right)$

$\mathrm{irr}≔0.4458188048$

$\mathrm{Duration}\left(\mathrm{cashflow2}\,\mathrm{irr}\right)$

$5.076090247$

$\mathrm{bond}≔\mathrm{FixedCouponBond}\left(100\,5\,\mathrm{Years}\,0.05\right)$

$\mathrm{bond}≔\mathbf{module}\left(\right)\mathbf{end\; module}$

$\mathrm{cflows}≔\mathrm{CashFlows}\left(\mathrm{bond}\right)$

$\mathrm{cflows}≔\left[\mathrm{5.\; on\; \text{'}January\; 1,\; 2006\text{'}}\,\mathrm{5.\; on\; \text{'}January\; 1,\; 2007\text{'}}\,\mathrm{5.\; on\; \text{'}January\; 1,\; 2008\text{'}}\,\mathrm{5.\; on\; \text{'}January\; 1,\; 2009\text{'}}\,\mathrm{5.\; on\; \text{'}January\; 1,\; 2010\text{'}}\,\mathrm{100.\; on\; \text{'}January\; 1,\; 2010\text{'}}\right]$

$\mathrm{Duration}\left(\mathrm{bond}\,0.03\,\mathrm{evaluationdate}=''January\; 5,\; 2000''\right)$

$9.556636250$

$\mathrm{Duration}\left(\mathrm{cflows}\,0.03\,\mathrm{evaluationdate}=''January\; 5,\; 2000''\right)$

$9.556636250$

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

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