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I am trying to roughly approximate (not really price) options on VIX futures whereby the VIX future is estimated using their bounds. If the option is approximated using the Black model, how do you determine the expiry T in the F(t,T) curve to use in the formula?

Alternatively, can you price the option by simulating the futures curve using a multivariate GBM? Any references?

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The expiry to T,t in any option model is simply the published expiry date on the exchange, at the close of trade. The time till expiry is simply the number of outstanding days till this occurrence, dates time is converted to a percentage of a year no of days / either 250 trading days OR 365 calendar days, that is another discussion, outside of this scope, whether trading days or calendar days. Both are used freely.

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  • $\begingroup$ Ahem! The expiration of VIX futures and options is on a Wednesday in the middle of the month (for example Vix Dec 2020 expires tomorrow Wednesday December 16. Not the third Friday. $\endgroup$
    – nbbo2
    Commented Dec 15, 2020 at 21:32
  • $\begingroup$ VIX expiries: macroption.com/vix-expiration-calendar Note that there are some 'irregular' expiries. $\endgroup$
    – user42108
    Commented Dec 16, 2020 at 0:59

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