Many software packages that report option Greeks (e.g., delta, gamma, theta, implied volatility) report incorrect values for VIX options (Fidelity, Schwab, Ameritrade , LIVEVOL and Barchart (free subscription) are notable exceptions). 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).

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:

VIX Index | True VIX option underlying (volatility future) | |

Underlying | 24.40 | 24.55 |

Delta | .86 | .91 |

Gamma | .11 | .09 |

IV | 143 | 82 (correct number) |

Hi Vance, I use Schwab’s SSE, and VIX options seem to be priced not correctly, showing intrinsic value for OTM options.

Option greeks are partial derivatives usually calculated under a Black Scholes or binomial model. These models do not apply to the VIX because it is mean reverting and options on it do not have to satisfy put-call parity (since you can’t actually trade the index). You can see this easily by the wide difference in implied volatilities for put and call options of the same strike. Normally, European options have to have very similar IV’s to satisfy put-call parity.

Its nice to recognize the true underlying is a futures contract and not the index itself, but the option greeks you get are still erroneous.

But deep OTM Calls and deep ITM put seem to comply with black scholes

Hi, I just responded to this comment. I agree with you that put/call parity works fine with VIX options if you use the correct underlying. Theta is problematic, but almost anything would be better than the current industry practice (except for LiveVol and perhaps a couple others) of using the VIX index as the underlying for their VIX Greek calculations.

— Vance

Hi Tom, I agree that Theta for VIX options does not follow Black / Scholes because of mean reversion, but I believe B&S delta / gamma calculations only need the log-normal distribution assumption, which I believe VIX futures, the true underlying exhibits. I think put/call parity works just fine with VIX optiond if you use the correct VIX future as the underlying.

— Vance

Tom, you are great! your points are not disputable, and the distribution of returns of the VIX future is far from log normal!