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Cap & Floor functions

The functions in this category compute price, risk management statistics ("Greeks") and implied volatilities for standard caps and floors using the Black-76 model. The functions receive array arguments to define the zero curve (curve dates and zero rates or discount factors). The Zero Curve Methodology section discusses the form of these arrays and relevant restrictions in greater detail. Any stubs are added to the beginning of the structure.


Cap_fix_strike_Black(argument list…)

Floor_fix_strike_Black(argument list…)

The calling functions allow the user to choose from six different calculations, indexed by an alphabetic Output_Type switch:

P option price
D delta (derivative with respect to forward yields)
G gamma (second derivative with respect to forward yields)
V vega (derivative with respect to volatility, 1% change)
T theta (time decay over next day)
I implied yield volatility

An Output_Type may be entered in either upper or lower case, and the user many substitute the entire word for the first letter if so desired (only the first letter is scanned). Delta and gamma are returned in terms of changes in prices. The price, vega, and theta are in terms of percentage of the notional of the structure.

The functions use the following arguments:

Argument Description Restrictions
Output_Type output returned by function P, D, G, V, T or I (see above)
Valuation_Date valuation date (e.g. today) valid Excel date number
Start_Date original start date of the cap/floor valid Excel date number
= Valuation_Date for spot start
> Valuation_Date for forward start
< Valuation_Date for seasoned
Term_in_Months term of the cap/floor in months relative to Start_Date > 0 (integer)
Cap_Rate or Floor_Rate strike rate of the cap/floor in decimal form (e.g. six percent entered as 0.06) > 0
Frequency number of caplets/floorlets per year 1, 2, 4, or 12
Year_Basis year basis used in determining payments 360 or 365
Holidays array of holiday dates valid Excel date numbers
strictly ascending order
Date_Convention business date convention 0 = no adjustment
1 = Following business day
2 = Modified following
3 = Previous
Zero_Dates array of zero coupon curve dates strictly ascending order
The first date of this array must be Valuation_Date
Zero_Rates array of continuously compounded riskless rates in decimal form (e.g. six percent entered as 0.06) corresponding to Zero_Dates > 0
Yield_Vol
or
Opt_Val
yield volatility in decimal form, or market price of the cap/floor (when Output_Type = I) > 0
Last_Reset_Rate last reset rate on the cap/floor in decimal form (used only if an existing caplet/floorlet reset has passed) >= 0
(argument ignored if Start_Date is greater than Valuation_Date)
if <= 0, caplets/floorlets before the Valuation_Date are ignored

CapFloor_fix_strike_Black(argument list…)

This function is identical to those above, except that there is an extra argument (at the beginning of the argument list) which permits the user to choose between three different types of structures using a CapFloor_Type alphabetic switch:

C cap
F floor
S straddle (combination of cap + floor)

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