calculate the price of an interest rate instrument using the Black model
BlackPrice(instrument, discountrate, volatility)
cap, floor, collar or swaption; financial instrument
non-negative constant or a yield term structure; discount rate
non-negative constant; volatility
equations of the form option = value where option is one of referencedate or daycounter; specify options for the BlackPrice command
daycounter = a string containing a date specification in a format recognized by ParseDate or a Date data structure -- This option specifies a day counter or day counting convention.
referencedate = a string containing a date specification in a format recognized by ParseDate or a Date data structure -- This option specifies the reference date, that is, the date when the discount factor is 1. By default this is set to the global evaluation date.
The BlackPrice command computes the price of an interest rate instrument (such as Cap, Floor, Collar or InterestRateSwap) using the Black model with the specified discount rate and volatility.
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.
nominalamt ≔ 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⁡nominalamt,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 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
The Finance[BlackPrice] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
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