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I would like to model VIX futures. The aim is not pricing but risk management. Thus I want to get risk measures like volatility right and be able to accurately calculate correlations when the VIX futures is analyzed in portfolio context.

I am not sure whether the Heston approach that is sometimes used is suitable for this aim. Another approach would be to approximate the VIX futures by the historical returns of the VIX index.

What is the approach most useful in risk management? Do you know any useful software implementation for VIX (e.g. in R)?

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  • $\begingroup$ I have only seen VIX-Futures modelled like equity index futures in commercial risk models. This is certainly wrong as it neglects the term strucutre of implied varianze/volatility. Have you ever seen a commercial model doing something better? $\endgroup$
    – Richi Wa
    Commented Sep 18, 2012 at 9:11
  • $\begingroup$ Did you work out a model on VIX futures? I am working on a similar problem. How can I contact you to ask a few questions? For example, how do you use historic VIX index to approximate VIX future price? Thanks. $\endgroup$
    – user4775
    Commented Feb 12, 2013 at 6:35
  • $\begingroup$ Hi ITGuy ... you have made a comment out of your answer and by that deleted my comment. I repeat: Bloomberg e.g. offers time series representing so called generic futures. This is UX1 for the VIX futures with approx. 1 month time to maturity, UX2 for 2 months and so on. Thus these time series represent the history of a constant maturity futures. When I need to model a traded VIX-futures, then I map it to the generic ones (this mapping changes as the futures approaches maturity) and use the returns of the generic futures in the historical simulation. $\endgroup$
    – Richi Wa
    Commented Feb 12, 2013 at 12:44
  • $\begingroup$ are you sure that UX1 is a 1 month constant maturity? At least on my bloomberg settings it simply points to the "next" future, and therefore it jumps to the next contract on expiration date. Therefore it is not quite a constant maturity instrument. $\endgroup$
    – mbison
    Commented Mar 4, 2019 at 16:13
  • $\begingroup$ @mbison this is what I mean by "approx." 1 month ... in the sense that you describe. It points to the first which has a maturity between something like 0 and 1 month ... right? only in this sense. $\endgroup$
    – Richi Wa
    Commented Mar 4, 2019 at 20:32

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Your idea of using the empirical (historical) distribution makes the most sense for risk management.

For one thing, it ensures you are working with real-world probabilities, whereas obtaining a distribution from an option pricing model (say by fitting Heston to the VIX options) would put you in risk-neutral probability space. For another, the common stochastic vol models all do a poor job of matching VIX dynamics.

Now, any continuous stochastic process looks like a brownian motion in sufficiently short timespans. So the commercial providers are not necessarily crazy to model VIX like equity index futures. However, the dynamics of VIX can be far jumpier than equity index futures, and so I think they are making a mistake by ignoring that aspect.

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  • $\begingroup$ Thanks for your answer. What I meant with equity index futures was the cost of carry pricing. This is certainly wrong for VIX futures. The reason is that $VIX^2$ is a portfolio of options but $VIX$ ist the square root of that portfolio. So the pricing logic of equity index futures does not apply. $\endgroup$
    – Richi Wa
    Commented Sep 19, 2012 at 7:22
  • $\begingroup$ I have checked data and the historical approach seems to work - but one has to use constant maturity indices with the maturity matching the maturity of the futures (approximately). This seems to work fine. I just wonder what to do in the last days of the life of the futures. The convergence to the VIX spot seems to be quite slow on a price basis and does not happen on a return basis. $\endgroup$
    – Richi Wa
    Commented Sep 20, 2012 at 11:08
  • $\begingroup$ I'm not quite sure why VIX spot is part of your system at all. It's not like it's going to be part of your portfolio, so for my money it makes sense to exclusively consider the dynamics of the futures, which likely don't change much even in the last few days beforfe expiration. It would at least be worth checking that notion, since you would get a useful simplification. $\endgroup$
    – Brian B
    Commented Sep 20, 2012 at 14:53
  • $\begingroup$ Thanks for your comment, @Brian B. I thought about using the VIX as proxy close to maturity because after all the futures settles against VIX (although trading stops the night before and the futures settles against some kind of opening price on the next day, details can be found on the CBOE website). But, yes, I don't see good results in doing this. I should stick to the constant maturity data and leave VIX spot out of the game. $\endgroup$
    – Richi Wa
    Commented Sep 20, 2012 at 15:31

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