Getting the correct greeks for VIX options


Most software packages that report option greeks (e.g., delta, gamma, theta, implied volatility) report incorrect values for VIX options. 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 true underlying is the corresponding VIX future for that month (e.g., January VIX futures for January VIX options).

Chris McKhann notes that LIVEVOL provides free delayed quotes that include correctly computed greeks for VIX options.

You can compute reasonably accurate Greek values for VIX options yourself. You don’t even have to get a futures quote (although you can get delayed quotes for free). It turns out that if you split the bid/ask price for the 10 strike VIX option and add 10 to it you can get close, usually within +-.15 to the true price for the VIX options. You can then use freely available options calculators to compute your IV based on the underlying price and option price and then your.  One example :

True VIX Option Underlying = 10+ 14.55 (bid/asked split of VIX option with strike price of 10) is 14.20/14.90) = 24.55
Closing price of 22.5 Call 1.85/2.2 (assume 2.10) for value
___________ VIX index __  True VIX option underlying
Underlying ____ 24.40 ____ 24.55
Delta _________ .86 ______ .91
Gamma _______ .11 _______ .09
IV ___________ 143 ______ 82 (very close to the actual 20 day historic volatility)

Normally the VIX index and the true VIX option underlying are further 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 broker quoted VIX option — they are usually lying about the underlying.
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