Hedging VIX Options with Corresponding VX Futures
Summary
The document describes how standard VIX option delta is generally measured against the corresponding maturity VX futures contract rather than spot VIX. It outlines a first order hedge calculation that accounts for both the option’s delta and the difference in contract multipliers. In the example, two calls at 50 delta correspond to roughly one tenth of a standard VX future, so selling a whole future would leave a substantial short hedge.
The hedge is approximate and applies to standard VIX options before expiration. These are European, cash settled options whose final settlement is based on the VIX special opening quotation; they are not literally options on futures. A separate product consists of options on VX futures, where the futures contract is the actual underlying. The document gives a calculation and product distinctions, but no empirical performance evidence or discussion of how the hedge changes as market conditions evolve.
Key ideas
- Standard VIX option delta is typically referenced to the matching VX futures contract rather than spot VIX.
- A futures hedge must account for option delta and the ratio of contract multipliers.
- Two 50 delta calls are approximately one tenth of a standard VX future by the stated contract conventions.
- Standard VIX options are cash settled and have final settlement tied to the VIX special opening quotation.
- Options on VX futures are a distinct product with the futures contract as the underlying.
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Full text
# Are a VIX option's delta with respect to their underlying futures?
# Are a VIX option's delta with respect to their underlying futures?
EX. does a May 19th 50d call move with respect to the May futures contract? If so would going long 2 50d calls and shorting the underlying future neutralise the delta?
## Answer by carry_and_pray (score 1)
https://quant.stackexchange.com/a/85589
Yes, typically, the value of a standard VIX option is taken with respect to the corresponding VX futures contract and NOT the spot VIX. CBOE states in its guidance that the delta of a VIX option is determined relative to the price of the corresponding VX future. For example, September VIX options versus September VX futures. Also, a VX future has delta 1000 in CBOE's contract-size convention while a VIX option's unit delta ranges from 0 to 100.
So, the hedge is not long 2 calls and short 1 future since the contract sizes are different. A VIX option has multiplier 100 while a standard VX future has multiplier 1000 so the first order hedge ratio is, $$ N_F = N_\text{opt} \times \Delta \times \frac{100}{1000}, $$ when $\Delta$ is quoted on the usual 0 to 1 scale. For two calls with $\Delta = 0.50$ then, $$ N_F \approx 2 \times 0.50 \times \frac{100}{1000} = 0.1. $$ So two 50-delta calls hedge about 1/10th of one standard VX future and not one full future. Shorting one full future would over-hedge the positive by about a factor of ten. The equivalent statement in CBOE's unit-delta convention is that two 50-delta calls have a total delta of 100 while one VX future has delta 1000.
The other subtlety is that standard VIX options are still not literally options on VX futures. They are European, cash-settled VIX index options, and final settlement is to the VIX SOQ on expiration morning. That is why people often say they are “priced off” the corresponding future rather than spot VIX: spot VIX itself is not tradable, and the matching future is the natural hedge instrument before expiration.
CBOE also launched a separate product called options on VIX futures. For those, the underlying really is a VX future. That is a different product from the traditional VIX options.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.