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Finance

  

Convexity

  

calculate the convexity of a set of cash flows or a bond

 

Calling Sequence

Parameters

Options

Description

Examples

Compatibility

Calling Sequence

Convexity(cashflows, rate, opts)

Convexity(bond, rate, opts)

Parameters

cashflows

-

data structure created using the SimpleCashFlow constructor or a list of such data structures; cash flows

bond

-

fixed or floating rate bond data structure; bond

rate

-

non-negative real number; interest rate

opts

-

equations of the form option = value where option is one of evaluationdate, compounding or daycounter; specify options for the Convexity 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 given interest rate.

• 

daycounter = a name representing a supported day counter (e.g. ISDA, Simple) or a day counter data structure created using the DayCounter constructor -- This option provides a day counter which will be used to convert the period between two dates as a fraction of the year.

• 

evaluationdate =  a string containing a date specification in a format recognized by ParseDate or a date data structure -- This option specifies the evaluation date. By default this is set to the global evaluation date (see EvaluationDate).

Description

• 

The Convexity command calculates the convexity of a set of cash flows or a bond.

• 

For a set of cash flows C[i]t the convexity is defined as

it2C[i]tPtiC[i]tPt

  

where Pt is the discount factor at time t implied by the given interest rate.

• 

A bond's convexity is defined as the weighted second derivative of the price function with respect to the interest rate:

ⅆ2ⅆr2BrBr

• 

The parameter cashflows is a cash flow or a list of cash flows (see FixedRateCoupon, InArrearIndexedCoupon, ParCoupon, SimpleCashFlow, or UpFrontIndexedCoupon).

• 

The parameter bond must be a fixed- or floating-rate bond data structure (see FixedCouponBond, FloatingRateBond, ZeroCouponBond).

Examples

withFinance:

SetEvaluationDateJan-01-2005:

paymentdateJan-02-2007

paymentdate:=Jan-02-2007

(1)

cashflow1SimpleCashFlow100,paymentdate

cashflow1:=100. on January 2, 2007

(2)

Convexitycashflow1,0.03,evaluationdate=Jan-01-2005

4.010966410

(3)

Convexitycashflow1,0.03,evaluationdate=Jan-01-2004

9.016445862

(4)

Here is another example.

nominalamt100

nominalamt:=100

(5)

rate0.05

rate:=0.05

(6)

paymentdateJan-01-2015

paymentdate:=Jan-01-2015

(7)

startdateJan-01-2006

startdate:=Jan-01-2006

(8)

enddateJan-01-2010

enddate:=Jan-01-2010

(9)

couponFixedRateCouponnominalamt,rate,startdate,enddate,paymentdate

coupon:=20. on January 1, 2015

(10)

Compute the value of this cash flow on January 01, 2005.

Convexitycoupon,0.03,evaluationdate=Jan-01-2005

100.

(11)

Here is an example using bonds.

bondFixedCouponBond100,5,Years,0.05

bond:=moduleend module

(12)

cflowsCashFlowsbond

cflows:=5. on 'January 1, 2006',5. on 'January 1, 2007',5. on 'January 1, 2008',5. on 'January 1, 2009',5. on 'January 1, 2010',100. on 'January 1, 2010'

(13)

Convexitybond,0.03,evaluationdate=Jan-05-2000

92.45245571

(14)

Convexitycflows,0.03,evaluationdate=Jan-05-2000

92.45245571

(15)

Compatibility

• 

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

• 

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

See Also

Finance[CompoundFactor]

Finance[DiscountFactor]

Finance[Duration]

Finance[EvaluationDate]

Finance[FixedRateCoupon]

Finance[InArrearIndexedCoupon]

Finance[NetPresentValue]

Finance[ParCoupon]

Finance[SetEvaluationDate]

Finance[SimpleCashFlow]

Finance[UpFrontIndexedCoupon]

Finance[ZeroCurve]

 


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