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, We present for each index the plots of the logarithm of the SQP ratios against the annualized volatility (MAD)
Real data FIGURE A.4: The logarithm of ES ratios as a function of annualized volatility (on real data) for ? = 95%. From left to right ,
, GARCH
The logarithm of ES ratios as a function of annualized volatility (on sample paths from GARCH(1,1) simulations with Gaussian innovations) for ? = 95%. From left to right, vol.5 ,
, A.5.2 SQP ratios and annualized volatility (MAD)
, We see the mean of 1000 repetitions, and its corresponding empirical 2.5% and 97.5% quantiles. From left to right, top to bottom, the estimation methods are: Zumbach, fGARCH, rugarch
, Estimation Quality: Beta value FIGURE E.3: Parameter estimates of beta for sample 1 with the different methods
, Estimation Quality: Alpha value FIGURE E.5: Parameter estimates of alpha in sample 2 with the different methods
, We see the mean of 1000 repetitions, and its corresponding empirical 2.5% and 97.5% quantiles, Estimation Quality: Beta value FIGURE E, vol.6
Overall summary On real data we observed the following (although not presented here, but only in the online-appendix ,
, ? In general all methods behave similarly (and sensitive) to changes in the data set