| Popis: |
In this thesis, the Heston-Nandi GARCH(1,1) (henceforth, HN-GARCH) option pricing model is fitted via 4 maximum likelihood-based estimation and calibration approaches using simulated returns and/or options. The purpose is to examine the benefits of the joint estimation using both returns and options over the fundamental returns-only estimation on GARCH models. From our empirical studies, with the additional option sample, we can improve the efficiency of the estimates for HN-GARCH parameters. Nonetheless, the improvements for the risk premium factor, both from empirical standard errors, and sample RMSEs, are insignificant. In addition, option prices are simulated with a pre-defined noise structure and with different noise levels, to demonstrate the consequence when we have a noisy option sample versus a less noisy one. The result shows that, with added option samples the RMSEs for estimated GARCH parameters are reduced dramatically, even with a very noisy option data set. This suggests that calibrating GARCH option pricing models with a relatively short return series of around 6 years, plus an option sample is more ideal than using a long return series of 20 years alone. Finally, as a by-product, we studied which type of options leads to the larger calibration improvements. Our controlled experiment confirms that out-of-the-money, short-maturity options are the best choices. |
