Estimating the fair value of options based on ARIMA–GARCH models with errors distributed according to the Johnson's $S_U$ law

In continuation of the article ‘`Risk-neutral dynamics for the ARIMA–GARCH (autoregressive integrated moving average – generalized autoregressive conditional heteroskedasticity) random process with errors distributed according to the Johnson’s $S_U$ law," this paper presents the experimental results for the ARIMA–GARCH (autoregressive integrated moving average – generalized autoregressive conditional heteroskedasticity) models with normal (N), exponential beta of the second type (EGB2), and $S_U$ Johnson (JSU) error distributions. The fair value of European options is estimated by the Monte-Carlo method based on the results obtained in the specified article by using the extended Girsanov principle. The parameters of the ARIMA–GARCH-N, ARIMA–GARCH-EGB2, and ARIMA–GARCH-JSU models were found by the quasi-maximum likelihood method. The efficiency of the resulting risk-neutral models was studied using the example of European exchange-traded options PUT and CALL on basic assets DAX and Light Sweet Crude Oil.