Getting the correct greeks for VIX options

Many software packages that report option Greeks (e.g., delta, gamma, theta, implied volatility) report incorrect values for VIX options (LIVEVOL is a notable exception). Depending on the date and state of the market they can vary from almost correct to widely wrong–giving truly nonsense numbers.  These packages assume that the VIX index is the underlying for the VIX options.  This is wrong.  The best underlying to use is the corresponding VIX future for that month (e.g., January VIX futures for January VIX options).  Fidelity and Ameritrade get partial credit because they don’t use the VIX as the underlying, but they don’t appear to use the best VIX futures quote for their underlying.

You can compute reasonably accurate delta and gamma values for VIX options yourself. You don’t even have to get a futures quote (although you can get CFE delayed quotes for free). It turns out that if you add 10 to the $10 strike VIX call option you are pretty close to the true price of the underlying volatility futures.  Since the bid / ask spreads for these options tend to be pretty wide, you should split the bid/ask price.  This should get you within +-0.15 of the true price.  Then you can use options calculators to compute your IV and other Greeks based on the underlying price and option price.  One example:

$10 Strike  VIX option price is:   bid 14.20 / asked 14.90.  Splitting the difference gives: 14.55
True VIX Option Underlying = 10+ S10 VIX option price = 24.55
Closing price of S22.5 VIX Call  bid 1.85, asked 2.2 (splitting this spread gives 2.10).
VIX Index True VIX option underlying (volatility future)
Underlying 24.40 24.55
Delta .86 .91
Gamma .11 .09
IV 143 82 (correct number)
Normally the VIX index and the true VIX option underlying are farther apart, so the IV differences are even larger, but in this example, there was only one more trading day for the options so the index and true underlying are converging.
So beware of brokers quoting VIX option greeks—they are usually lying about the underlying.

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