GARCH,EGARCH,NAGARC​H,GJR models and implicit VIX

Estimate GARCH/EGARCH/NAGARCH/GJR parameters from a time series of prices , rates and VIX value.

The functions in this file can be used for estimate historical pararameters of GARCH/EGARCH/GJR/NAGARCH models using time series of prices, rates and CBOE VIX. There are three types of loglikehood functions that are maximize. The first one uses returns only. The second one uses VIX levels only and the last one uses both.

In an article of Zhang and Hao [2013:http://jfec.oxfordjournals.org/content/early/2013/01/20/jjfinec.nbs026.short?rss=1] are described some formulas to calculate implicit VIX. The Functions in the zip file can be used to calculate implicit VIX for GARCH/EGARCH/GJR/NAGARCH models using such formulas. It is also possibible make a graph in which there are market VIX and implicit VIX.

Another exercise that can be done is simulate and plot a VIX futures term structure using impliciti VIX and market VIX.

The Last exercise is a calibration of parameters. Starting from a date, the function can estimate parameters in-sample of GARCH/EGARCH/GJR/NAGARCH models minimize the difference bewteen implicit VIX and market VIX. Then VIX futures term structures can be simulated and compared with out-of-sample real market VIX futures structures.

In garchmodel there is an example.

These codes are in Object-Orientend Programming language. There are two macroclass :'Models' and Futures'. There are four classes, one for each model.
Inside Zip file, there is a diagram with properties and methods of the classes.