Creates a SABR curve to model the dynamics of the volatility curve (smile).
There are 4 market inputs to this model.
ATM vol (This is really a 'SABR' volatility value to satisfy the model, but you can input the market ATM volatility and calibrate for the other 3 parameters - see the
CalibrateSABR() function.
This is a ‘volatility-like’ parameter, not equal to the volatility, but there is a functional relationship between this parameter and the at the money (ATM) volatility.), BETA (or SKEW, a value between zero and one [0,1] which determines the relationship between futures spot and at the money (ATM) volatility.
SKEW = 1 indicates that the user believes that if the market were to move up or down in an orderly fashion, the ATM volatility level would not be significantly affected (lognormal like).
Beta less than one (1) indicates that if the market were to move then ATM volatility would move in the opposite direction (normal like))), ALPHA (Is the volatility of volatility, a model feature which acknowledges that volatility obeys well known clustering in time.
It controls the wings of the smile curve, the higher the value the more wingy the smile), RHO (Correlation between rates and vols).
This SABR model is identical to that of the same model developed by Hagan, Kumar, Lesniewski and Woodward (2002) except that we denote the ALPHA parameter as the 'volatility of volatility' (or WING) parameter and 'ATMVol' (alpha in the case of their model) as our ‘volatility-like’ parameter.
Each of the four SABR parameters inputs can either be a matrix (range input) or a single value (numeric value).
If a matrix, rows are option maturities (Tenors), columns are Underlying lengths (Tenor format).
You must decorate the volatility matrix with header and row information.
Row headers are option Maturity tenors from the calculation date, Column headers are Underlying length values (Tenor format).
If one prefers to enter a single value (thus this volcurve will represent the smile for only one underlying and one option maturity), you simply pass this in as a single value.
Forward rates are also inputs to the SABR model, but these will be acquired during the valuation of a deal (the YieldCurve will be obtained internally).
You also indicate via the 'DepoIndex' (for deposit underlying) and 'Swap Index' (for swap underlying) parameters the details of the underlying tenors.
This information will be used during risk management process (see the
CapeTools IR Risk category of functions).
This function creates an object and returns a string-key value to represent this created object.
The TAG value of the string-key returned (second part of the key) is : "SABRVC"
- Key parameter
Key value to use as a handle for the created object
- Reload parameter
When creating this object for the first time, set this parameter to a positive value. Within Excel, when re-computing a worksheet where you do not wish to recreate the object, set this parameter to zero (0).
- CurveName parameter
A tag used to identify this curve (case insensitive) if placed within a Volatility curve collection ( via the
GroupedVolCurves() function ). If you pass in an empty string, it will default to the name of the 'Key' parameter.
- ValueDate parameter
Key to an already created Valuation Date Object. (Via the
ValueDateObj() function).
- SettleDays parameter
Number of days between the Exercise date of the options and the STARTDATE of the instrument.
- ATMRange parameter
A matrix of SABR volatility values (greater than zero (0)) including header information, or a single point (flat) value. This is really a 'SABR' volatility value to satisfy the model, but you can input the market ATM volatility and calibrate for the other 3 parameters - see the
CalibrateSABR() function. This is a ‘volatility-like’ parameter, not equal to the volatility, but there is a functional relationship between this parameter and the at the money (ATM) volatility.
- ALPHARange parameter
A matrix of SABR alpha values (greater than zero (0)) including header information, or a single point (flat) value.
- BETARange parameter
A matrix of SABR beta values (between 0.0 (normal distribution) and 1.0 (lognormal distribution)) including header information, or a single point (flat) value.
- RHORange parameter
A matrix of SABR correlation (between -1 and 1) values including header information, or a single point (flat) value.
- DivideVolBy100 parameter
Is the input volatility entered as a percentage value (true), or the raw volatility value (false). If entered as a percentage, the value will be divided by 100.0 internally.
- DepoIndex parameter
Deposit (Libor) Index Template Key. (Created via the
CreateDepoTemplate() function). This is the minimum definition of an interest rate index ( ie - LIBOR ) and is the one used by the curve. The definition of the index underlying a cap or floor structure instrument is defined via this template (minus the 'Tenor' information).
- SwapIndex parameter
Swap Index Template Key. (Created via the
CreateSwapTemplate() function). This object provides the minimum definition of an interest rate Swap and is the one used by the curve. If this curve allows for Swap type instrument as the underlyings (via Tenors) as inputs, then the definition of those instruments are specified via this template.
- DayCount parameter
DayCounter for converting dates into year fractions.
- InterpType parameter
Interpolation method to use when interpolating the curve for vols, - LINEAR, LOGLINEAR, CUBIC.
The C# example below contains all the sub-function calls leading up to this function call. As a result, the example can contain a lot of code.
The VB.NET, J#, C++.NET, Java, Excel VBA, Visual Basic 6 (via COM) and C++ examples below contain function code stubs for the calls leading up to this function call. However, the function call for this function is displayed.
You can easily reproduce the stub functions code from the
C# example.
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Function Syntax