create new interest rate collar
Collar(floatingleg, caprates, floorrates)
list of floating-rate coupons; floating leg
non-negative number or a list of non-negative numbers; cap rates
non-negative number or a list of non-negative numbers; floor rates
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
N is the nominal value,
dTi is the year fraction between dates Ti−1 and Ti,
P⁡Ti 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.
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.
SetEvaluationDate⁡November 17, 2006:
November 17, 2006
The nominal amount is 100.
nominal ≔ 100
Create a 6-month EURIBOR benchmark rate with a forecasted rate of 5%. No history is available for this rate.
benchmark ≔ BenchmarkRate⁡6,Months,EURIBOR,0.05
benchmark ≔ moduleend module
Construct a discount interest rate curve.
discount_curve ≔ ForwardCurve⁡0.05,'daycounter'=Actual360
Construct floating leg payments.
start_date ≔ AdvanceDate⁡2,Days
start_date≔November 19, 2006
end_date ≔ AdvanceDate⁡start_date,20,Years,'convention'=ModifiedFollowing
end_date≔November 19, 2026
coupon_dates ≔ seq⁡AdvanceDate⁡start_date,6⁢i,Months,i=0..40:
floating_leg ≔ seq⁡ParCoupon⁡nominal,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 ≔ Cap⁡floating_leg,0.07
ir_cap ≔ moduleend module
ir_floor ≔ Floor⁡floating_leg,0.03
ir_floor ≔ moduleend module
ir_collar ≔ Collar⁡floating_leg,0.07,0.03
ir_collar ≔ moduleend module
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 ≔ BlackPrice⁡ir_cap,0.05,0.2
floor_price ≔ BlackPrice⁡ir_floor,0.05,0.2
collar_price ≔ BlackPrice⁡ir_collar,0.05,0.2
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.
The Finance[Collar] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
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