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Finance[Collar] - create new interest rate collar

Calling Sequence

Collar(floatingleg, caprates, floorrates)

Parameters

floatingleg

-

list of floating-rate coupons; floating leg

caprates

-

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

floorrates

-

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

Description

• 

The Collar command creates a new interest rate collar with the specified parameters. This is a combination of a long position in the corresponding interest rate cap and a short position in the corresponding interest rate floor.

• 

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

NdTiPTiCi`+`CiPTi`+`

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,

– 

Ci is the fixed cap rate at time Ti,

– 

Fi is the fixed floor rate at time Ti.

• 

The parameter floatingleg defines floating rate coupon payments. The parameters caprates and floorrates define the corresponding fixed rates. The first cap/floor rate corresponds to the first floating-rate coupon, the second cap/floor 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 a 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)

ir_floor:=Floorfloating_leg,0.03

ir_floor:=moduleend module

(8)

ir_collar:=Collarfloating_leg,0.07,0.03

ir_collar:=moduleend module

(9)

Price these instruments using the Black model with a discount rate of 5% and a volatility of 20%, and verify that the price of the cap is equal to the sum of of the prices of the other two instruments.

cap_price:=BlackPriceir_cap,0.05,0.2

cap_price:=6.832847321

(10)

floor_price:=BlackPriceir_floor,0.05,0.2

floor_price:=2.642595692

(11)

collar_price:=BlackPriceir_collar,0.05,0.2

collar_price:=4.190251628

(12)

cap_price=floor_price+collar_price

6.832847321=6.832847320

(13)

See Also

Finance[Collar], Finance[Floor]

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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