Calibration Category Group



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  1. CapeTools One-Dimensional Solvers


    General Description

    Functions to construct One-Dimensional Optimization objects needed by the 'CapeTools Option Solver' category of functions.

    The following One-Dimensional Optimization objects can be created :

    • Bisection()
    • Brent()
    • FalsePosition()
    • Newton()
    • Ridder()
    • Secant()


    The Newton() solver requires that the first derivative function of the function being solved upon to be implemented. Fortunatly, we have already done this for all the functions present within the 'CapeTools Option Solver' category of functions. Within these objects, you can set minimum and maximum starting values as well as a tolerance level.


  2. CapeTools Calibration Tools


    General Description

    Functions to construct Multi-Dimensional Optimization objects needed by all the calibration functions.

    The following Optimization objects can be created :

    • Simplex() (Multi-dimensional simplex object)
    • LevenbergMarquardt() (Multi-dimensional LevenbergMarquardt object (based on MINPACK))
    • ConjugateGradient() (Multi-dimensional Conjugate Gradient object)
    • SteepestDescent() (Multi-dimensional Steepest Descent object)


    We would recommend using the LevenbergMarquardt() followed by the Simplex() functions as these are very stable multi-dimensional solvers.


  3. CapeTools Calibration Instruments


    General Description

    Functions to help construct calibration instruments.

    The following calibration utility functions can be used to help generate swaption calibration dates.

    • GenStartDiagOSDates()
    • GenEndDiagOSDates()


    The following interest rate calibration functions create arrays of calibration instruments.

    • CFCalibInst() (for an array of Caplet/Floorlet instruments)
    • CFCalibInst2() (for an array of Caplet/Floorlet instruments)
    • CFCalibInst3() (for an array of Caplet/Floorlet instruments)
    • CapFloorCalibInst() (for an array of CapFloor instruments)
    • OSCalibInst1() (for an array of Swaption instruments)
    • OSCalibInst2() (for an array of Swaption instruments)
    • OSCalibInst3() (for an array of Swaption instruments)
    • MixedCalibInst() (for an array of both Swaption and Caplet/Floorlet instruments)
    • MixedCalibInst2() (for an array of both Swaption and Caplet/Floorlet instruments)

  4. CapeTools SABR Calibration


    General Description

    Functions to calibrate the parameters of the SABR volatility model (ATMVol, Alpha, Beta and Rho).

    The following SABR calibration functions create arrays of calibration instruments.

    • SABRCalibInst()
    • SABRCalibInst2()
    • SABRCalibInst3()


    The actual SABR calibration is conducted via the CalibrateSABR() or CalibrateSABR2() functions and used to populate the following SABR functions.

    • SABRVolCurve() (requires matrices of calibrated SABR parameters for interest rate instruments).
    • EquitySABRVolCurve()


    Within the CalibrateSABR() function, you can actually fix any of the four parameters and solve for the others.

    Note: 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.
    Note: We treat the 'ATMVol' parameter within our functions as the At-The-Money market volatility. However the SABR model actually treats this as some 'Beta' or 'SABR' volatility. In practice one can set this value to the ATMVol and solve for the other parameters. However if you are fixing some of the parameters of the SABR model except the 'ATMVol' parameter before calibrating, you may find that the ATMVol parameter that is implied out is not the At-The-Money market volatility. You may also find this to be the case when using the ConjugateGradient() or SteepestDescent() multi-dimensional optimization objects. In these cases the interpretation of the ATMVol is no longer the At-The-Money market volatility but some 'Beta' or 'SABR' volatility to correspond with the SABR model.

  5. CapeTools Heston Calibration


    General Description


    Functions for calibrating the parameters of the following Heston, Bates models :


    • Heston model
    • Bates model
    • Bates Double-Exponential Jump Diffusion with Deterministic Jump Intensity model
    • Bates Log-Normal Jump Diffusion with Deterministic Jump Intensity model
    • Bates Double-Exponential Jump Diffusion model


    You can selectively fix the values of some of the parameters and calibrate the others.

  6. CapeTools LMM Calibration


    General Description

    Functions to calibrate the parameters of the Libor Market Model objects.

    • CalibrateModelLFM() (Calibrates the linear exponential volatility parameters of a Forward Libor Market Model given a list of calibration instruments)
    • CalibrateModelLFM_2() (Calibrates the linear exponential volatility parameters of a Forward Libor Market Model given a list of calibration instruments)


    Parameters calibrated from the CalibrateModelLFM() and CalibrateModelLFM_2() functions can be passed to the LiborMarketModel() or LiborMarketModel2() functions.


  7. CapeTools IR Calibration


    General Description

    Functions to calibrate the parameters of the interest rate model objects.

    The interest rate calibrations are conducted via the following functions.

    • CalibrateModelG2() (Calibrates the parameters of a G2 interest rate ShortRateModel via a G2 2 Factor Swaption Engine)
    • CalibrateModelG2_2() (Calibrates the parameters of a G2 interest rate ShortRateModel via a G2 2 Factor Swaption Engine)
    • CalibrateModelJAM() (Calibrates the parameters of an interest rate ShortRateModel (ie HullWhite, Vasicek) via a Jamshidian Swaption Engine)
    • CalibrateModelJAM_2() (Calibrates the parameters of an interest rate ShortRateModel (ie HullWhite, Vasicek) via a Jamshidian Swaption Engine)
    • CalibrateModelOSTree() (Calibrates the parameters of an interest rate ShortRateModel (ie BlackKarasinski, HullWhite, Vasicek, G2) via a Tree Swaption Engine)
    • CalibrateModelOSTree_2() (Calibrates the parameters of an interest rate ShortRateModel (ie BlackKarasinski, HullWhite, Vasicek, G2) via a Tree Swaption Engine)
    • CalibrateModelCFTree() (Calibrates the parameters of an interest rate ShortRateModel (ie BlackKarasinski, HullWhite, Vasicek, G2) via a Tree CapFloor Engine)
    • CalibrateModelCFTree_2() (Calibrates the parameters of an interest rate ShortRateModel (ie BlackKarasinski, HullWhite, Vasicek, G2) via a Tree CapFloor Engine)
    • CalibrateModelCFAnalytic() (Calibrates the parameters of an interest rate ShortRateModel (ie HullWhite, Vasicek, G2) via a Analytical CapFloor Engine)
    • CalibrateModelCFAnalytic_2() (Calibrates the parameters of an interest rate ShortRateModel (ie HullWhite, Vasicek, G2) via a Analytical CapFloor Engine)
    • CalibrateModelCFOS() (Calibrates the parameters of an interest rate ShortRateModel (ie BlackKarasinski, HullWhite, Vasicek, G2) via various user defined pricing engines)
    • CalibrateModelCFOS_2() (Calibrates the parameters of an interest rate ShortRateModel (ie BlackKarasinski, HullWhite, Vasicek, G2) via various user defined pricing engines)

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