Master of Science
Statistics and Actuarial Sciences
Dr. Reginald J. Kulperger
Option pricing is a major area in financial modeling. Option pricing is sometimes based on normal GARCH models. Normal GARCH models fail to capture the skewness and the leptokurtosis in financial data. The variant GARCH-in-mean (GARCH-M) model is widely used in the option pricing literature. It adds a heteroskedasticity term to the mean equation, which is interpreted as a risk premium, and also incorporates a type of asymmetry.
Our goal is to compare option valuation between GARCH-M and ARMA-GARCH models with normal and non-normal, z-distributed innovations. The models are fitted to the historical return data, and risk neutral measures are based on the conditional Esscher transform and the extended Girsanov principle. We compare European Calls on the S&P 500 with the model predictions. The TGARCH is best for ARMA-GARCH/GARCH-M models. Neither normal nor z dominates the other, but overall z-TGARCH-M (z-innovations) seems to be best, ARMA- TGARCH is surprisingly good.
Xi, Yi, "Comparison of option pricing between ARMA-GARCH and GARCH-M models" (2013). Electronic Thesis and Dissertation Repository. 1215.