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.