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Why VIX Options Can Have Deltas Far from One Half

Article Quant Q&A · Author: mikea
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Summary

The document asks why a VIX option described as at the money can have a delta far from one half, unlike a typical stock option. The answer distinguishes spot-based at-the-money options from at-the-money-forward options. A contract struck at the forward level is the relevant reference point for a delta near one half; a strike at the current VIX spot may be far from that forward level.

For stocks, the forward and spot levels are often relatively close, so the distinction may be less visible. VIX futures can differ substantially from spot, making an option that is at the money by spot appear materially away from the money relative to its forward. The post illustrates this with quoted VIX levels for different expiries, but it provides no general pricing derivation or delta calculation. The explanation is a conceptual clarification, and the size and direction of the effect depend on the forward curve and contract maturity.

Key ideas

  • An option at the spot price need not be at the forward price.
  • An at-the-money-forward option is the reference associated with roughly one-half delta.
  • VIX futures can differ substantially from the VIX spot level.
  • The spot-forward gap can help explain unusual deltas in VIX options.

Tags

OptionsVolatilityDerivatives pricing
Full text
# VIX ATM Options Delta


# VIX ATM Options Delta












VIX ATM options seem to have delta that is very far from .5 (.18/.82 for 60dte now) with .5 being in 30 territory.

Why is this very different from stock options? Why is atm put much less sensitive to the underlying change comparing to a typical stock?

## Answer by MainCom (score 3, accepted)

https://quant.stackexchange.com/a/61237

It is the at the money forward (ATMF) contract rather the at the money (ATM) contract that has roughly 0.5 delta. For stocks the difference is not so big between the ATMF and ATM contract since $F = Se^{(r-d)t}$. However, this is not the case for VIX. For example, the forward (future) of VIX is now around 30 for the April contract (which has 63 days to expiration) versus 22.81 for the February (which expired today).

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.