A survey and implementation of some calibration algorithms for the SABR and Heston models
This thesis surveys and implements some calibration methods for the SABR and Heston models. Hagan (2002) examined the effect of the SABR parameters on the skew in order to determine which parameters may be redundant. Hagan andWest (2005) found that by fixing one of the parameters in the SABR model, the remaining parameters were stable over time. We implement a SABR calibrator to confirm that the parameters are stable over time. We then examine the effects of the five Heston parameters on the skew in order to determine if any of the parameters are redundant. Calibrators where some parameters have been fixed and calibrators where no parameters have been fixed are implemented. The performance of these calibrators is then compared based on three criteria: the stability of the parameters over time, the fit of the solution and the computational efficiency of the calibrator. We find that the Heston parameters are more stable if the redundant parameters are fixed, the computation time is less and the fit is slightly worse. All implementations are done in the context of the South African market. The calibrators are programmed in Matlab and the code is included in the appendix.
Networked Digital Library of Theses and Dissertations