Electronic Thesis and Dissertation Repository

Thesis Format

Monograph

Degree

Master of Science

Program

Statistics and Actuarial Sciences

Supervisor

Escobar-Anel, Marcos

2nd Supervisor

Stentoft, Lars

Co-Supervisor

Abstract

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.

Summary for Lay Audience

The development of option pricing models has been a productive research area ever since the first Nobel prize-winning proposal of the Black-Scholes-Merton model in the 1970s. In 2000, Heston and Nandi proposed a particular GARCH$(p,q)$ conditional volatility model with a closed-form option pricing formula for European option prices. The filtering and estimation of conditional volatility of this model can be completed solely from daily observables. Yet, many questions remain unanswered. For instance, is the model calibration process robust and reliable? How accurate and valid are the parameter estimates? In this thesis, we simulated market data based on the Heston Nandi-GARCH(1,1) model, and then examined and compared the 4 maximum likelihood-based estimation and calibration approaches using returns and/or options. We first followed Bollerslev (1986) and Heston and Nandi (2000) to investigate the fundamental returns-only estimation on GARCH models, during which we found that the price of risk parameter, is particularly difficult to estimate from returns data only, and its estimator is highly influenced by the average level of simulated daily noises. Hence, we simulated option prices with a pre-defined noise structure, calibrated the model jointly with options data, and compared its performance with the benchmark returns-only MLE method. We conjectured beforehand that bringing in option data shall help calibrate all parameters, with the potential of capturing the risk premium more precisely. 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, we simulated the option sample 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.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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