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Finance[BlackPrice] - calculate the price of an interest rate instrument using the Black model
Calling Sequence
BlackPrice(instrument, discountrate, volatility)
Parameters
instrument
-
cap, floor, collar or swaption; financial instrument
discountrate
non-negative constant or a yield term structure; discount rate
volatility
non-negative constant; volatility
opts
equations of the form option = value where option is one of referencedate or daycounter; specify options for the BlackPrice command
Description
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.
Options
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.
Compatibility
The Finance[BlackPrice] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
Examples
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.
The nominal amount is 100.
Create a 6-month EURIBOR benchmark rate with a forecasted rate of 5%. No history is available for this rate.
Construct a discount interest rate curve.
Construct floating-leg payments.
Construct an interest rate cap with a fixed cap rate of 7% for all payments in the floating leg.
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.
See Also
Finance[CompoundFactor], Finance[DiscountFactor], Finance[FixedRateCoupon], Finance[InArrearIndexedCoupon], Finance[ParCoupon], Finance[SimpleCashFlow], Finance[UpFrontIndexedCoupon], Finance[ZeroCurve]
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