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Finance

  

EquivalentRate

  

calculate equivalent interest rate

 

Calling Sequence

Parameters

Options

Description

Examples

References

Compatibility

Calling Sequence

EquivalentRate(rate, old, new, interval)

EquivalentRate(rate, old, new, startdate, enddate, opts)

Parameters

rate

-

positive constant, list or Vector; given interest rate

old

-

Annual, Bimonthly, Continuous, EveryFourthMonth, Monthly, Quarterly, Semiannual, Simple, SimpleThenAnnual, SimpleThenBimonthly, SimpleThenEveryFourthMonth, SimpleThenMonthly, SimpleThenQuarterly, or SimpleThenSemiannual; compounding type for the original interest rate

new

-

Annual, Bimonthly, Continuous, EveryFourthMonth, Monthly, Quarterly, Semiannual, Simple, SimpleThenAnnual, SimpleThenBimonthly, SimpleThenEveryFourthMonth, SimpleThenMonthly, SimpleThenQuarterly, or SimpleThenSemiannual; compounding type for the desired interest rate

interval

-

non-negative constant, list(non-negative), or Vector; duration of the compounding interval in years

startdate

-

a string containing a date specification in a format recognized by ParseDate or a date data structure; start of the compounding interval

enddate

-

a string containing a date specification in a format recognized by ParseDate or a date data structure; end of the compounding interval

opts

-

equation of the form option = value where option is daycounter; specify options for the EquivalentRate command

Options

• 

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

Description

• 

The EquivalentRate command calculates an equivalent rate for the specified compounding interval and compounding type. The parameter rate is the original rate. It must be a positive constant. The old and new parameters are the original compounding type and the new compounding type respectively. The parameter interval is the duration of the compounding period. Alternatively, one can specify the beginning and the end of the compounding period as dates.

• 

The optional parameter interval can be used to specify the length of the compounding interval in years. This parameter is relevant only when the conversion involves simple compounding.

Examples

withFinance:

rate10.06:

rate2EquivalentRaterate1,Continuous,Monthly

rate2:=0.06015025031

(1)

evalfⅇrate1

1.061836547

(2)

evalf1+rate21212

1.061836548

(3)

intervalL1.2,2.5,4.8:

ratelistEquivalentRate0.65,Continuous,Simple,intervalL

ratelist:=0.9845602212485011.631367614872034.50966242566154

(4)

This is an example of converting from/to simple compounding.

startdateJan-05-2006

startdate:=Jan-05-2006

(5)

enddateDec-31-2006

enddate:=Dec-31-2006

(6)

intervalYearFractionstartdate,enddate

interval:=0.9863013699

(7)

Settingsdaycounter

Historical

(8)

EquivalentRaterate1,Continuous,Simple,interval

0.06181088722

(9)

EquivalentRaterate1,Continuous,Simple,Jan-05-2006,Jan-05-2007,daycounter=ISMA

0.06183654655

(10)

Here are more conversions.

rate3EquivalentRaterate1,Continuous,Quarterly

rate3:=0.06045225846

(11)

rate4EquivalentRaterate2,Monthly,Quarterly

rate4:=0.06045225846

(12)

rate5EquivalentRaterate1,Continuous,Simple,1.0

rate5:=0.06183654655

(13)

EquivalentRaterate5,Simple,Continuous,1.0

0.06000000000

(14)

EquivalentRaterate1,Continuous,Simple,5.0

0.06997176152

(15)

References

  

Brigo, D., Mercurio, F., Interest Rate Models: Theory and Practice. New York: Springer-Verlag, 2001.

  

Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.

  

Kellison, S.G., Theory of Interest, 2nd edition, Irwin: McGraw-Hill, 1991.

Compatibility

• 

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

• 

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

See Also

Finance[CompoundFactor]

Finance[DiscountCurve]

Finance[DiscountFactor]

Finance[ForwardCurve]

Finance[ForwardRate]

Finance[ImpliedRate]

Finance[ParRate]

Finance[ZeroCurve]

 


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