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Finance[Cap] - create new interest rate cap

Calling Sequence

Cap(floatingleg, exerciserates)

Parameters

floatingleg

-

list of floating-rate coupons; floating leg

exerciserates

-

non-negative number or a list of non-negative numbers; exercise rates

Description

• 

The Cap command creates a new interest rate cap instrument with the specified parameters. This instrument can be viewed as a payer interest rate swap where each exchange payment is executed only if it has positive value. (see Brigo and Mercurio (2001) for more details).

• 

Assume that we have a set of coupon payments to occur at the times T1, T2, ..., Tn. At each time instance Ti the cap pays

NdTiPTiKi`+`

where

– 

N is the nominal value,

– 

dTi is the year fraction between dates Ti1 and Ti,

– 

PTi is a coupon payment at the time Ti,

– 

Ki is the fixed rate at time Ti.

• 

The parameter floatingleg defines floating-rate coupon payments. The parameter exerciserates defines the corresponding fixed rates. The first exercise rate corresponds to the first floating rate coupon, the second exercise rate corresponds to the second floating rate coupon, etc. If the size of the exerciserates list is smaller than the size of the floatingleg list then the last exercise rate will be used for all the remaining coupons.

• 

The LatticePrice command can be used to price an interest rate cap using any given binomial or trinomial tree. The BlackPrice command will compute the price of an interest rate cap using the Black model.

Examples

withFinance:

Set the global evaluation date. This date is taken as the reference date for all yield curves and benchmark rates unless another date is specified explicitly.

SetEvaluationDateNovember 17, 2006:

EvaluationDate

November 17, 2006

(1)

The nominal amount is 100.

nominal:=100

nominal:=100

(2)

Create a 6-month EURIBOR benchmark rate with forecasted rate of 5%. No history is available for this rate.

benchmark:=BenchmarkRate6,Months,EURIBOR,0.05

benchmark:=moduleend module

(3)

Construct a discount interest rate curve.

discount_curve:=ForwardCurve0.05,'daycounter'=Actual360

discount_curve:=moduleend module

(4)

Construct floating leg payments.

start_date:=AdvanceDate2,Days

start_date:=November 19, 2006

(5)

end_date:=AdvanceDatestart_date,20,Years,'convention'=ModifiedFollowing

end_date:=November 19, 2026

(6)

coupon_dates:=seqAdvanceDatestart_date,6i,Months,i=0..40:

floating_leg:=seqParCouponnominal,discount_curve,coupon_datesi,coupon_datesi+1,i=1..40:

Construct an interest rate cap with a fixed cap rate of 7% for all payments in the floating leg.

ir_cap:=Capfloating_leg,0.07

ir_cap:=moduleend module

(7)

Price this instrument using the Black model with a discount rate of 5% and a volatility of 20%.

BlackPriceir_cap,0.05,0.2

6.832847321

(8)

See Also

Finance[BlackPrice], Finance[Collar], Finance[FixedRateCoupon], Finance[Floor], Finance[InArrearIndexedCoupon], Finance[InterestRateSwap], Finance[LatticePrice], Finance[ParCoupon], Finance[SimpleCashFlow], Finance[UpFrontIndexedCoupon]

References

  

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

  

Glasserman, P., Monte Carlo Methods in Financial Engineering. New York: Springer-Verlag, 2004.

  

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


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