EquitySABRVolCurve

Creates an equity/FX/commodity SABR object to model the dynamics of the volatility curve (smile).

There are 5 market inputs to this model.

ATM vol (This is really a 'SABR' volatility column to satisfy the model, but you can input the market ATM volatility and calibrate for the other 3 parameters - see the CalibrateSABR() function), 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) and finally FWD (The forward price of the underlying at the option dates).

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.

The main SABR matrix input to this function, 'SABRMatrix' parameter, consists of option maturity rows along with five columns each representing a parameter of the SABR model (Thus 6 columns in total).

You must decorate the SABR volatility matrix with header and row information.

Row headers are option Maturity tenors from the calculation date.

The five column headers are 'ATM', 'ALPHA', 'BETA', 'RHO' and 'FWD'. You can use a combination of the SABRCalibInst() and CalibrateSABR() functions in order to calibrate the parameters (Alpha, Beta, Rho) of the SABR model.

ArgName	ArgType	IsKey
Key	String	FALSE
Reload	Long	FALSE
ValueDate	String	TRUE
SettleDays	Long	FALSE
SABRMatrix	Range	FALSE
DivideVolBy100	Boolean	FALSE
BusDayConv	BDCEnum	FALSE
DayCount	DayCountEnum	FALSE
Cal	String	TRUE
InterpType	InterpEnum	FALSE

The first column represents the name of the parameters. The second column specifies whether the parameters are optional or not. Finally the last column provides some sample input data.
Function call input string-keys are always in the format : "NAME.EXTTAG.TICKER" The "EXTTAG.TICKER" part is determined from the output of other, capetools, object creation functions.

ArgName	IsOptional (Excel only)	Example
Key	FALSE	MyEquitySABRVolCurve
Reload	FALSE	1
ValueDate	FALSE	ValueDateNAME.EXTTAG.TICKER (from a function call)
SettleDays	FALSE	2
SABRMatrix	FALSE	EquitySABRVolCurve_SABRMatrix_Range (creates a range object)
DivideVolBy100	FALSE	true
BusDayConv	FALSE	ModifiedFollowing
DayCount	FALSE	30360
Cal	FALSE	CalNAME.EXTTAG.TICKER (from a function call)
InterpType	TRUE	LINEAR

Example range for parameter : SABRMatrix

Within Excel, a range such as this can be passed directly into the SABRMatrix parameter.


Opt\SABR	ATM	ALPHA	BETA	RHO	FWD
3M	20.01	3.8	0.7	0.25	207.04
6M	20.02	3.8	0.7	0.25	215.04
9M	20.02	3.8	0.7	0.25	223.68
12M	20.03	3.81	0.7	0.25	229.31
2Y	20.04	3.81	0.7	0.25	237.12
3Y	20.05	3.81	0.7	0.25	247.11
4Y	20.06	3.81	0.7	0.25	253.04
5Y	20.07	3.81	0.7	0.25	261.81
6Y	20.08	3.81	0.7	0.25	267.77
7Y	20.09	3.81	0.7	0.25	277.48
8Y	20.09	3.82	0.7	0.25	282.77
9Y	20.1	3.82	0.7	0.25	290.6
10Y	20.11	3.82	0.7	0.25	295.62
11Y	20.12	3.82	0.7	0.25	301.61
12Y	20.13	3.82	0.7	0.25	306.96

Example C# API usage for setting the range data for parameter : SABRMatrix

CTQL.CTRangeData EquitySABRVolCurve_SABRMatrix = new CTQL.CTRangeData();

System.Text.StringBuilder EquitySABRVolCurve_SABRMatrix_builder =
new System.Text.StringBuilder(100);

EquitySABRVolCurve_SABRMatrix_builder.Append("{");
EquitySABRVolCurve_SABRMatrix_builder.Append("'Opt\\SABR'	 | ATM	 | ALPHA	 | BETA	 | RHO	 | FWD ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'3M'	 | 20.01	 | 3.8	 | 0.7	 | 0.25	 | 207.04 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'6M'	 | 20.02	 | 3.8	 | 0.7	 | 0.25	 | 215.04 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'9M'	 | 20.02	 | 3.8	 | 0.7	 | 0.25	 | 223.68 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'12M'	 | 20.03	 | 3.81	 | 0.7	 | 0.25	 | 229.31 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'2Y'	 | 20.04	 | 3.81	 | 0.7	 | 0.25	 | 237.12 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'3Y'	 | 20.05	 | 3.81	 | 0.7	 | 0.25	 | 247.11 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'4Y'	 | 20.06	 | 3.81	 | 0.7	 | 0.25	 | 253.04 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'5Y'	 | 20.07	 | 3.81	 | 0.7	 | 0.25	 | 261.81 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'6Y'	 | 20.08	 | 3.81	 | 0.7	 | 0.25	 | 267.77 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'7Y'	 | 20.09	 | 3.81	 | 0.7	 | 0.25	 | 277.48 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'8Y'	 | 20.09	 | 3.82	 | 0.7	 | 0.25	 | 282.77 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'9Y'	 | 20.1	 | 3.82	 | 0.7	 | 0.25	 | 290.6 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'10Y'	 | 20.11	 | 3.82	 | 0.7	 | 0.25	 | 295.62 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'11Y'	 | 20.12	 | 3.82	 | 0.7	 | 0.25	 | 301.61 ;");
EquitySABRVolCurve_SABRMatrix_builder.Append("'12Y'	 | 20.13	 | 3.82	 | 0.7	 | 0.25	 | 306.96");
EquitySABRVolCurve_SABRMatrix_builder.Append("}");

// Parse the string into the Range object.
EquitySABRVolCurve_SABRMatrix.RangeFromStr( EquitySABRVolCurve_SABRMatrix_builder.ToString() );