 FixedRateCoupon - Maple Help

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Finance

 FixedRateCoupon
 construct a fixed rate coupon on a term structure Calling Sequence FixedRateCoupon(nominal, rate, startdate, enddate, paymentdate, opts) Parameters

 nominal - non-negative constant; nominal value rate - non-negative constant; coupon rate startdate - a string containing a date specification in a format recognized by ParseDate or a date data structure; accrual start date enddate - a string containing a date specification in a format recognized by ParseDate or a date data structure; accrual end date paymentdate - a string containing a date specification in a format recognized by ParseDate or a date data structure; payment date opts - equations of the form option = value where option is daycounter; specify options for the FixedRateCoupon command Options

 • daycounter = Actual360, Actual365Fixed, AFB, Bond, Euro, Historical, ISDA, ISMA, OneDay, Simple, Thirty360BondBasis, Thirty360EuroBondBasis, Thirty360European, Thirty360Italian, Thirty360USA, or a day counter data structure; convention used to convert the amount of time between two dates to year fractions Description

 • The FixedRateCoupon command constructs a coupon paying a fixed interest rate on the given date.
 • The interest is accrued between startdate and enddate based on simple compounding.
 • The optional parameter paymentdate can be used to specify when the accrued interest will be payed. By default paymentdate is equal to enddate. Examples

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

First set the global evaluation date to January 1, 2005.

 > $\mathrm{SetEvaluationDate}\left("January 01, 2005"\right):$
 > $\mathrm{EvaluationDate}\left(\right)$
 ${"January 1, 2005"}$ (1)

Construct a coupon that pays the fixed rate of 5%. The accrual period starts on January 3, 2006 and ends on January 3, 2010.

 > $\mathrm{nominal}≔100$
 ${\mathrm{nominal}}{≔}{100}$ (2)
 > $\mathrm{rate}≔0.05$
 ${\mathrm{rate}}{≔}{0.05}$ (3)
 > $\mathrm{paymentdate}≔"Jan-03-2015"$
 ${\mathrm{paymentdate}}{≔}{"Jan-03-2015"}$ (4)
 > $\mathrm{startdate}≔"Jan-03-2006"$
 ${\mathrm{startdate}}{≔}{"Jan-03-2006"}$ (5)
 > $\mathrm{enddate}≔"Jan-03-2010"$
 ${\mathrm{enddate}}{≔}{"Jan-03-2010"}$ (6)
 > $\mathrm{coupon}≔\mathrm{FixedRateCoupon}\left(\mathrm{nominal},\mathrm{rate},\mathrm{startdate},\mathrm{enddate},\mathrm{paymentdate}\right)$
 ${\mathrm{coupon}}{≔}{\mathrm{20. on January 3, 2015}}$ (7)

Compute the value of this cash flow on January 3, 2005.

 > $\mathrm{NetPresentValue}\left(\mathrm{coupon},0.03\right)$
 ${14.81392905}$ (8)

Here is another way to compute this. First, compute the accrued interest.

 > $\mathrm{accrued}≔\mathrm{nominal}\mathrm{CompoundFactor}\left(\mathrm{rate},\mathrm{enddate},\mathrm{referencedate}=\mathrm{startdate},\mathrm{compounding}='\mathrm{Simple}'\right)-\mathrm{nominal}$
 ${\mathrm{accrued}}{≔}{20.0000000}$ (9)

This is the value to be received on January 3, 2010. You must discount this value using the discount rate.

 > $\mathrm{accrued}\mathrm{DiscountFactor}\left(0.03,\mathrm{paymentdate}\right)$
 ${14.81392905}$ (10)

This is the value of the same cash flow on January 3, 2004.

 > $\mathrm{NetPresentValue}\left(\mathrm{coupon},0.03,\mathrm{referencedate}="Jan-03-2004"\right)$
 ${14.37846821}$ (11)
 > $\mathrm{nominal}\left(\mathrm{CompoundFactor}\left(\mathrm{rate},\mathrm{enddate},\mathrm{referencedate}=\mathrm{startdate},\mathrm{compounding}='\mathrm{Simple}'\right)-1\right)\mathrm{DiscountFactor}\left(0.03,\mathrm{paymentdate},\mathrm{referencedate}="Jan-03-2004"\right)$
 ${14.37846821}$ (12)

Calculate the net present value of the set of two cash flows.

 > $\mathrm{rate2}≔0.07$
 ${\mathrm{rate2}}{≔}{0.07}$ (13)
 > $\mathrm{startdate2}≔"Jan-03-2007"$
 ${\mathrm{startdate2}}{≔}{"Jan-03-2007"}$ (14)
 > $\mathrm{enddate2}≔"Jan-03-2010"$
 ${\mathrm{enddate2}}{≔}{"Jan-03-2010"}$ (15)
 > $\mathrm{coupon2}≔\mathrm{FixedRateCoupon}\left(\mathrm{nominal},\mathrm{rate2},\mathrm{startdate2},\mathrm{enddate2},\mathrm{paymentdate}\right)$
 ${\mathrm{coupon2}}{≔}{\mathrm{21.00000000 on January 3, 2015}}$ (16)
 > $\mathrm{NetPresentValue}\left(\left[\mathrm{coupon},\mathrm{coupon2}\right],0.03\right)$
 ${30.36855455}$ (17)
 > $\mathrm{NetPresentValue}\left(\mathrm{coupon},0.03\right)+\mathrm{NetPresentValue}\left(\mathrm{coupon2},0.03\right)$
 ${30.36855455}$ (18) Compatibility

 • The Finance[FixedRateCoupon] command was introduced in Maple 15.