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Finance

  

ForwardRate

  

compute forward rates based an a given term structure

 

Calling Sequence

Parameters

Options

Description

Examples

References

Compatibility

Calling Sequence

ForwardRate(termstructure, maturitytime, opts)

ForwardRate(termstructure, maturitydate, opts)

ForwardRate(termstructure, expirytime, maturitytime, opts)

ForwardRate(termstructure, expirydate, maturitydate, opts)

Parameters

termstructure

-

yield term structure; term structure

maturitytime

-

non-negative constant; maturity time in years

expirytime

-

non-negative constant; expiry time in years

maturitydate

-

non-negative constant; maturity date

expirydate

-

non-negative constant; expiry date

opts

-

Equations of the form option = value where option is compounding; specify options for the ForwardRate command

Options

• 

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

Description

• 

The ForwardRate(termstructure, expirytime, maturitytime) and ForwardRate(termstructure, expirytime, maturitytime) calling sequences return the forward interest rate for the specified expiry and maturity. 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.

• 

The ForwardRate(termstructure, maturitytime) and ForwardRate(termstructure, maturitytime) calling sequences calculate an approximation of the instantaneous forward interest rate for the maturity maturitytime or maturitydate based on the specified term structure.

Examples

withFinance:

times0,0.5,1,1.5,2:

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

RZeroCurvetimes,rates,interpolation=LogLinear:

ForwardRateR,0.0,0.5

0.04000000000

(1)

ForwardRateR,0.1,0.5

0.04205582119

(2)

ForwardRateR,1.5

0.08448956888

(3)

plots[display]plot'ForwardRate'R,0.1,t,t=0.5..2,color=blue,thickness=3,plot'ForwardRate'R,0.3,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)

ForwardRateR1,1.0

0.05000000000

(5)

ForwardRateR1,0.5,1.5

0.05000000000

(6)

ForwardRateR1,Jan-05-2007

0.04999999999

(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 the monthly compounding.

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

R2Jan-05-2005

0.04989612178

(9)

R21.0

0.04989612178

(10)

ForwardRateR2,0.5,1.0

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:

ForwardRateR3,0.5,1.0

0.07000000000

(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[ForwardRate] command was introduced in Maple 15.

• 

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

See Also

Finance[DiscountCurve]

Finance[ForwardCurve]

Finance[ParRate]

Finance[ZeroCurve]

Finance[ZeroRate]

 


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