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Pricing of VIX futures is complicated, because it is not possible to use a standard hedging argument to get a value similar to stock futures.

What different approaches for pricing VIX futures exist? Which ones are used in practice by traders and others?

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1 Answer

The best theoretical model for pricing vix futures and options is a variance gamma model. However in practice that class of models is difficult to get robust results...

In practice, most floor traders in vix products base their hedging off of the SPX option chain. Vix is calculated from those options, in the first place, so this approach makes intuitive sense. Isolating the variance component of those the SPX options is straightforward using several approaches, and does not require much sophisticated numerical work.

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Thanks very much for your very interesting answer! I have a follow-up question: VIX futures are not possible to replicate using SPX options? (although the VIX itself is) So in principle this should not give a good pricing model? Do you have some suggested article for which pricing model to use? –  zoom Dec 6 '11 at 17:18
    
Theoretically, any future can be replicated with a bank account and the underlying. In practice, in this case however, the difference in expiry and settlement make that kind of direct replication infeasible, without basis risk. As I said, a good theoretical model to use is variance gamma. A good approach to use in practice is to use the options on SPX. Also not a precise hedge/pricing instrument, but very liquid which cuts out a lot of risk. You can find some articles about both of these issues on the CBOE's website. –  glyphard Dec 20 '11 at 15:29
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@glyphard Respectfully disagree. Theoretically, and practically VIX futures cannot be replicated - VIX index is calculated as a square root of a basket of options. Square root is a non-linear transformation, making arbitrage impossible. Hedging off SPX options is quite risky - this is not your regular basis risk - the basis in SPX/VIX is nonlinear with its own set greeks, and VIX traders that I know do not use SPX for hedging, but rather trade in the entire VIX futures and options product suite, since in the VIX options are the dominant market with much greater volume. –  onlyvix.blogspot.com May 23 '12 at 19:22
    
+1 there is no static replication for the vix... You can literally disperse over the entire vola complex in the spx.. vix futures, vix options, SPX options, all the constituents of the SPX (IE baskets of idiosyncratic risk) short systemic in the index and long idiosyncratic is one.. Model-less valuations can be generated from the most liquid part of the term structure by valuating every thing against the most liquid back month.. like 3 month.. and flatting everything to that figure.. –  cdcaveman Feb 17 '13 at 5:47
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