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Finance[BlackPrice] - calculate the price of an interest rate instrument using the Black model
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Calling Sequence
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BlackPrice(instrument, discountrate, volatility)
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Parameters
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instrument
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cap, floor, collar or swaption; financial instrument
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discountrate
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non-negative constant or a yield term structure; discount rate
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volatility
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non-negative constant; volatility
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opts
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equations of the form option = value where option is one of referencedate or daycounter; specify options for the BlackPrice command
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Description
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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.
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Options
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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.
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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.
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Compatibility
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The Finance[BlackPrice] command was introduced in Maple 15.
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Examples
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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.
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The nominal amount is 100.
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Create a 6-month EURIBOR benchmark rate with a forecasted rate of 5%. No history is available for this rate.
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Construct a discount interest rate curve.
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Construct floating-leg payments.
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![coupon_dates := [seq(AdvanceDate(start_date, 6*i, Months), i = 0 .. 40)]](/support/helpjp/helpview.aspx?si=8852/file01580/math192.png)
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![floating_leg := [seq(ParCoupon(nominalamt, discount_curve, coupon_dates[i], coupon_dates[i+1]), i = 1 .. 40)]](/support/helpjp/helpview.aspx?si=8852/file01580/math196.png)
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Construct an interest rate cap with a fixed cap rate of 7% for all payments in the floating leg.
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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.
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Download Help Document
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