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Finance

  

ZeroRate

  

compute zero rates based on a given term structure

 

Calling Sequence

Parameters

Options

Description

Examples

References

Compatibility

Calling Sequence

ZeroRate(termstructure, maturitytime, opts)

ZeroRate(termstructure, maturitydate, opts)

Parameters

termstructure

-

yield term structure; term structure

maturitytime

-

non-negative constant; maturity time in years

maturitydate

-

date in any of the formats recognized by the Finance[ParseDate] command; maturity date

opts

-

equation of the form option = value where option is compounding; specify option for the ZeroRate command

Options

• 

compounding = Simple, Continuous, Annual, Semiannual, EveryFourthMonth, Quarterly, Bimonthly, Monthly, SimpleThenAnnual, SimpleThenSemiannual, SimpleThenEveryFourthMonth, SimpleThenQuarterly, SimpleThenBimonthly, or SimpleThenMonthly -- This option specifies compounding type for the returned rate. The default value is Continuous.

Description

• 

The ZeroRate command returns the zero interest rate for the maturity maturitytime or maturitydate based on the specified term structure. The parameter termstructure can be a zero curve, a discount curve, or a forward curve. The compounding type for the returned rate can be controlled through the corresponding option.

Examples

withFinance:

times0,0.5,1,1.5,2:

rates0.03,0.04,0.06,0.07,0.075:

RZeroCurvetimes,rates,interpolation=LogLinear:

ZeroRateR,0.5

0.04000000000

(1)

ZeroRateR,1.0

0.06000000000

(2)

ZeroRateR,1.5

0.07000000000

(3)

plot'ZeroRate'R,t,t=0.5..2,color=blue,thickness=3,axes=BOXED,gridlines=true

In this example, create a flat zero curve with reference date set to January 5, 2006.

R1ZeroCurve0.05,referencedate=Jan-05-2006:

R11.0

0.05000000000

(4)

ZeroRateR1,1.0

0.05000000000

(5)

ZeroRateR1,1.5

0.05000000000

(6)

ZeroRateR1,Jan-05-2007

0.05000000000

(7)

TYearFractionJan-05-2006,Jan-05-2007,R1:-daycounter

T:=1.

(8)

In this example, create a zero curve with the same parameters as above but assume that the interest rate is based on monthly compounding.

R2ZeroCurve0.05,compounding=Monthly,referencedate=Jan-05-2005:

R2Jan-05-2005

0.04989612178

(9)

R21.0

0.04989612178

(10)

ZeroRateR2,1.0

0.04989612178

(11)

In this example, create a zero curve based on a piecewise interpolation of zero rates. Use the default interpolation.

rates0.02,0.01,0.04,0.06,0.07:

times0.0,0.5,1.0,1.5,2.0:

R3ZeroCurvetimes,rates:

ZeroRateR3,1.0

0.04000000000

(12)

References

  

Brigo, D., Mercurio, F., Interest Rate Models: Theory and Practice. New York:

  

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

Compatibility

• 

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

• 

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

See Also

Finance[DiscountCurve]

Finance[EquivalentRate]

Finance[ForwardCurve]

Finance[ForwardRate]

Finance[ImpliedRate]

Finance[ParRate]

Finance[ZeroCurve]

 


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