LMMLinearExpVolModel2




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Creates a an extended linear-exponential volatility model for the libor market model.

The resulting object is to be passed as a parameter to the LiborMarketModel() function.

The extended linear exponential volatility model is defined as : sigma(t) = k_i*((b*(T{i}-t)+a)*exp{-c(T{i}-t)}+d), where T{i} is time at step i and k_i are weights that are applied to fixing (reset) value i (adjustment factors needed to match Black vols).

If you simply construct this object and leave the 'weights' parameter empty, the weights will be set to 1.0. Within the calibration functions (see CalibrateModelLFM() and CalibrateModelLFM_2() ) the weights will automatically be calibrated and from this, you can pass the calibrated values to the 'weights' parameter.

NOTE : If you are passing this object to the calibration functions along with an object created from the LMMProcess2() function, then these weights cannot be calibrated.

Basically only parameters from LMM processes started from spot can be calibrated (ie - the LMMProcess() function).



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 : "LMMLEVMOD2"



Note: Within Excel, the function is named - CT.MOD.LMMLinearExpVolModel2


High level graphic of LMMLinearExpVolModel2() function with parameters. Blue square node is the actual function with the parameters ordered.



Parameter Description


  1. Key parameter

    Key value to use as a handle for the created object
  2. 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).
  3. LMMProcess parameter

    Key to an already constructed LMMProcess object.
  4. a parameter

    'a' parameter that is to be used within the linear exponential volatility model.
  5. b parameter

    'b' parameter that is to be used within the linear exponential volatility model.
  6. c parameter

    'c' parameter that is to be used within the linear exponential volatility model.
  7. d parameter

    'd' parameter that is to be used within the linear exponential volatility model.
  8. weights parameter

    An optional array of weights (adjustment factors needed to match Black vols) that corresponds to each fixing rate generated within the LMMProcess() or LMMProcess2() object. If not provided the weights will simply be set to 1.0. You can apply a single value within the array that will be applied to all the fixing rates, you can also provide an array of length equal to that of the number of rates. Finally, if you provide an array of shorter length than the required number of rates, the final value will simply be used for the rest of the fixings. You can use the ABCDAdjFactors() function for a quick calibration of these weights.


Extended information

Function Syntax

VB Syntax 


String CTLMMVolCorrModels.LMMLinearExpVolModel2( _
String Key, _
Long Reload, _
String LMMProcess, _
Double a, _
Double b, _
Double c, _
Double d, _
Variant weights)


Excel Spreadsheet Syntax 


=CT.MOD.LMMLinearExpVolModel2(
Excel String Cell Key,
Excel Numeric Cell Reload,
Excel String Cell LMMProcess,
Excel Numeric Cell a,
Excel Numeric Cell b,
Excel Numeric Cell c,
Excel Numeric Cell d,
XLRange weights)


C++ Syntax 


static std::string LMMLinearExpVolModel2(
std::string Key,
long Reload,
std::string LMMProcess,
double a,
double b,
double c,
double d,
CTRangeDataCPP weights);


DotNET Syntax 


System.String CTLMMVolCorrModelsSA.LMMLinearExpVolModel2(
System.String Key,
System.Int32 Reload,
System.String LMMProcess,
System.Double a,
System.Double b,
System.Double c,
System.Double d,
CTRangeData weights);

Parameter data types

ArgNameArgTypeIsKey
KeyStringFALSE
ReloadLongFALSE
LMMProcessStringTRUE
aDoubleFALSE
bDoubleFALSE
cDoubleFALSE
dDoubleFALSE
weightsRangeFALSE

Example Inputs

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.


ArgNameIsOptional (Excel only)Example
KeyFALSEMyLMMLinearExpVolModel2
ReloadFALSE1
LMMProcessFALSELMMProcessNAME.EXTTAG.TICKER (from a function call)
aFALSE0.086592854
bFALSE0.105234154
cFALSE0.658891667
dFALSE0.06117745
weightsTRUELMMLinearExpVolModel2_weights_Range (creates a range object)


Example range for parameter : weights

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


Data is stored within the second column (Vector of data)..

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


CTQL.CTRangeData LMMLinearExpVolModel2_weights = new CTQL.CTRangeData();

System.Text.StringBuilder LMMLinearExpVolModel2_weights_builder =
new System.Text.StringBuilder(100);

LMMLinearExpVolModel2_weights_builder.Append("{");
LMMLinearExpVolModel2_weights_builder.Append("1 ;");
LMMLinearExpVolModel2_weights_builder.Append("0.93959593 ;");
LMMLinearExpVolModel2_weights_builder.Append("1.161423829 ;");
LMMLinearExpVolModel2_weights_builder.Append("1.136454663 ;");
LMMLinearExpVolModel2_weights_builder.Append("1.085602199 ;");
LMMLinearExpVolModel2_weights_builder.Append("1.00614192 ;");
LMMLinearExpVolModel2_weights_builder.Append("0.944104283 ;");
LMMLinearExpVolModel2_weights_builder.Append("0.886468038 ;");
LMMLinearExpVolModel2_weights_builder.Append("0.827628321 ;");
LMMLinearExpVolModel2_weights_builder.Append("0.897708504");
LMMLinearExpVolModel2_weights_builder.Append("}");

// Parse the string into the Range object.
LMMLinearExpVolModel2_weights.RangeFromStr( LMMLinearExpVolModel2_weights_builder.ToString() );


Example function usage


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.


If you are accessing this functrion via the MiniXL libraries, this function is present within the CT.QL.Models20 MiniXL Excel Addin.

Within our Excel Example Addin Generator, we have used the following QuantTools sub-functions in order to prepare the arguments needed to call the LMMLinearExpVolModel2() function. If you are executing this function via the MiniXL libraries, the module addin name, (in brackets, to the right of the sub-functions listed below), indicates the MiniXL library in which the sub-function is held. You will need to load this library into your Excel session (along with any other libraries that the sub-function call within the addin requires (ie - CT.QT.Utils20 addin in almost all cases) in order for the example to compute successfully.

These are the financial QuantTools sub-function calls that are used within the examples :





The objects generated by these sub-functions are inter-connected in the following way :




The following four examples demostrate calling this function within a Microsoft .NET environment

The following four examples demostrate calling this function within a non .NET environment

The following is a sample output from executing the LMMLinearExpVolModel2() function call


MyLMMLinearExpVolModel2_5.LMMLEVMOD2.0

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