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Finance

  

EuropeanSwaption

  

create a new European-style swaption

 

Calling Sequence

Parameters

Options

Description

Examples

References

Compatibility

Calling Sequence

EuropeanSwaption(irswap, exercise, opts)

Parameters

swap

-

simple swap data structures; interest rate swap

exercise

-

a non-negative constant, a string containing a date specification in a format recognized by Finance[ParseDate], or a date data structure; the maturity time or date

opts

-

(optional) equation(s) of the form option = value where option is one of referencedate or daycounter; specify options for the EuropeanSwaption command

Options

• 

referencedate = a string containing a date specification in a format recognized by Finance[ParseDate] or a date data structure -- This option provides the evaluation date. It is set to the global evaluation date by default.

• 

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 that will be used to convert the period between two dates to a fraction of the year. This option is used only if one of earliestexercise or latestexercise is specified as a date.

Description

• 

The EuropeanSwaption command creates a new European-style swaption with the specified payoff and maturity. The swaption can be exercised only at the time or date specified by the exercise parameter. This is the opposite of an American-style swaption, which can be exercised at any time before the expiration.

• 

The parameter swap is the underlying interest rate swap (see InterestRateSwap for more details).

• 

The parameter exercise specifies the time or date when the option can be exercised. It can be given either as a non-negative constant or as a date in any of the formats recognized by the Finance[ParseDate] command.

• 

The LatticePrice command can be used to price a European-style swaption using any given binomial or trinomial tree.

Examples

withFinance:

SetEvaluationDateNovember 17, 2006:

nominal1000.0

nominal1000.0

(1)

fixing_days2

fixing_days2

(2)

startAdvanceDate1,Years,EURIBOR

startNovember 17, 2007

(3)

maturityAdvanceDatestart,5,Years,EURIBOR

maturityNovember 17, 2012

(4)

discount_curveForwardCurve0.04875825,'daycounter'=Actual365Fixed

discount_curvemoduleend module

(5)

fixed_scheduleSchedulestart,maturity,Annual,'convention'=Unadjusted,'calendar'=EURIBOR

fixed_schedulemoduleend module

(6)

floating_scheduleSchedulestart,maturity,Semiannual,'convention'=ModifiedFollowing,'calendar'=EURIBOR

floating_schedulemoduleend module

(7)

benchmarkBenchmarkRate6,Months,EURIBOR,0.04875825

benchmarkmoduleend module

(8)

Construct an interest rate swap receiving the fixed-rate payments in exchange for the floating-rate payments.

swapInterestRateSwapnominal,0.0,fixed_schedule,benchmark,floating_schedule,0.0

swapmoduleend module

(9)

Compute the at-the-money rate for this interest rate swap.

atm_rateFairRateswap,discount_curve

atm_rate0.04995609574

(10)

Construct three swaps.

itm_swapInterestRateSwapnominal,0.8atm_rate,fixed_schedule,benchmark,floating_schedule,0.0

itm_swapmoduleend module

(11)

atm_swapInterestRateSwapnominal,1.0atm_rate,fixed_schedule,benchmark,floating_schedule,0.0

atm_swapmoduleend module

(12)

otm_swapInterestRateSwapnominal,1.2atm_rate,fixed_schedule,benchmark,floating_schedule,0.0

otm_swapmoduleend module

(13)

Here are cash flows for the paying leg of your interest rate swap.

cash_flowsCashFlowsitm_swap,paying

cash_flows39.97833882 on 'November 17, 2008',39.95141436 on 'November 17, 2009',39.96487659 on 'November 17, 2010',39.96487659 on 'November 17, 2011',39.97833882 on 'November 19, 2012'

(14)

Here are cash flows for the receiving leg of your interest rate swap.

CashFlowsitm_swap,receiving

24.55793340 on 'May 19, 2008',24.54222773 on 'November 17, 2008',24.59383300 on 'May 18, 2009',24.74716833 on 'November 17, 2009',24.47342475 on 'May 17, 2010',24.88406756 on 'November 17, 2010',24.47342475 on 'May 17, 2011',24.88406756 on 'November 17, 2011',24.55868130 on 'May 17, 2012',25.08832826 on 'November 19, 2012'

(15)

These are days when coupon payments are scheduled to occur.

datesmapt→tdate,cash_flows

datesdate,date,date,date,date

(16)

itm_swaptionEuropeanSwaptionitm_swap,AdvanceDatedates2,1,Days,EURIBOR

itm_swaptionmoduleend module

(17)

atm_swaptionEuropeanSwaptionatm_swap,AdvanceDatedates2,1,Days,EURIBOR

atm_swaptionmoduleend module

(18)

otm_swaptionEuropeanSwaptionotm_swap,AdvanceDatedates2,1,Days,EURIBOR

otm_swaptionmoduleend module

(19)

Price these swaptions using the Hull-White trinomial tree.

a0.048696

a0.048696

(20)

σ0.0058904

σ0.0058904

(21)

modelHullWhiteModeldiscount_curve,a,σ

modelmoduleend module

(22)

time_gridTimeGridYearFractionmaturity+0.5,100

time_gridmoduleend module

(23)

short_rate_treeShortRateTreemodel,time_grid

short_rate_treemoduleend module

(24)

Price your swaptions using the tree constructed above.

LatticePriceitm_swaption,short_rate_tree,discount_curve

9.794855431

(25)

LatticePriceatm_swaption,short_rate_tree,discount_curve

4.523445349

(26)

LatticePriceotm_swaption,short_rate_tree,discount_curve

1.502550032

(27)

You can also price these swaptions using an explicitly constructed trinomial tree.

ou_processOrnsteinUhlenbeckProcess0.04875,0.04875,1.0,0.3

ou_process_X

(28)

treeShortRateTreeou_process,time_grid

treemoduleend module

(29)

Price your swaptions using the second tree.

LatticePriceitm_swaption,tree,discount_curve

8.995305075

(30)

LatticePriceatm_swaption,tree,discount_curve

1.528598823

(31)

LatticePriceotm_swaption,tree,discount_curve

0.

(32)

References

  

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

Compatibility

• 

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

• 

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

See Also

Finance[BermudanSwaption]

Finance[BinomialTree]

Finance[BlackScholesBinomialTree]

Finance[BlackScholesTrinomialTree]

Finance[EuropeanSwaption]

Finance[GetDescendants]

Finance[GetProbabilities]

Finance[GetUnderlying]

Finance[ImpliedBinomialTree]

Finance[ImpliedTrinomialTree]

Finance[LatticeMethods]

Finance[LatticePrice]

Finance[SetProbabilities]

Finance[SetUnderlying]

Finance[StochasticProcesses]

Finance[TreePlot]

Finance[TrinomialTree]

 


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