I am currently researching the joint calibration problem of SPX and VIX. The idea is that: VIX options are derivatives on the VIX, which itself is derived from SPX options and should thus be able to be jointly calibrated.

Looking at European markets there is the STOXX50 and VSTOXX indices both of which are traded. However, on the VSTOXX index only options on futures on the VSTOXX itself are traded.

My question is, using the reasoning behind the SPX/VIX joint calibration, shouldn't the STOXX50 and VSTOXX be jointly calibrated, only that the VSTOXX instruments are options on futures?



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