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Finance

 ImpliedRate
 calculate an interest rate implied by the given compound factor

 Calling Sequence ImpliedRate(compound, interval, compounding) ImpliedRate(compound, startdate, enddate, compounding, opts)

Parameters

 compound - non-negative constant, list(non-negative), or Vector greater or equal to 1; compound factor interval - non-negative constant, list(non-negative), or Vector; length of the compounding interval in years compounding - Annual, Bimonthly, Continuous, EveryFourthMonth, Monthly, Quarterly, Semiannual, Simple, SimpleThenAnnual, SimpleThenBimonthly, SimpleThenEveryFourthMonth, SimpleThenMonthly, SimpleThenQuarterly, or SimpleThenSemiannual; compounding type for the desired interest rate 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 ImpliedRate 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 duration between two dates to year fractions.

Description

 • The ImpliedRate(compound, interval, compounding) calling sequence calculates an interest rate implied by the given compound factor, for the specified compounding interval and compounding type. The parameter compound is the compound factor; it should be a constant greater than or equal to 1. The parameter interval is the length of the compounding period.   These can also be entered as lists, in which case an array of their combinations is returned.  Alternatively, one can specify the compounding interval by giving the start date, end date and a day count convention. The compounding parameter is the compounding type.

Examples

 > $\mathrm{with}\left(\mathrm{Finance}\right):$
 > $\mathrm{rate1}≔0.06:$
 > $\mathrm{compound1}≔\mathrm{CompoundFactor}\left(\mathrm{rate1},1.0,\mathrm{compounding}=\mathrm{Monthly}\right)$
 ${\mathrm{compound1}}{≔}{1.061677812}$ (1)
 > $\mathrm{rate2}≔\mathrm{ImpliedRate}\left(\mathrm{compound1},1.0,\mathrm{Monthly}\right)$
 ${\mathrm{rate2}}{≔}{0.06000000013}$ (2)
 > $\mathrm{cmpdlist}≔\left[1.2,1.05,1.8\right]:$
 > $\mathrm{timelist}≔\left[0.2,2.5,3.2\right]:$
 > $\mathrm{ratelist}≔\mathrm{ImpliedRate}\left(\mathrm{cmpdlist},\mathrm{timelist},\mathrm{Monthly}\right)$
 ${\mathrm{ratelist}}{≔}\left[\begin{array}{ccc}{0.947127710385585}& {0.0731506799993591}& {0.0571109594056773}\\ {0.246447376629195}& {0.0195319441419981}& {0.0152566166050079}\\ {3.33009301168702}& {0.237433070376175}& {0.185096348508025}\end{array}\right]$ (3)
 > $\mathrm{rate3}≔\mathrm{ZeroCurve}\left(0.05,\mathrm{referencedate}="January 2, 2005"\right)$
 ${\mathrm{rate3}}{≔}{\mathbf{module}}\left({}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{end module}}$ (4)
 > $\mathrm{compound3}≔\mathrm{CompoundFactor}\left(\mathrm{rate3},"January 2, 2006"\right)$
 ${\mathrm{compound3}}{≔}{1.051271096}$ (5)
 > $\mathrm{ImpliedRate}\left(\mathrm{compound3},"January 2, 2005","January 2, 2006",\mathrm{Continuous}\right)$
 ${0.04999999964}$ (6)
 > $\mathrm{ImpliedRate}\left(\mathrm{compound3},"January 2, 2005","January 2, 2006",\mathrm{Monthly}\right)$
 ${0.05010431113}$ (7)
 > $\mathrm{ImpliedRate}\left(\mathrm{compound3},"January 2, 2005","July 5, 2005",\mathrm{Simple},\mathrm{daycounter}=\mathrm{Historical}\right)$
 ${0.1017062502}$ (8)
 > $\mathrm{ImpliedRate}\left(\mathrm{compound3},"January 2, 2005","July 5, 2005",\mathrm{Simple},\mathrm{daycounter}=\mathrm{Thirty360USA}\right)$
 ${0.1008611725}$ (9)

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[ImpliedRate] command was introduced in Maple 15.