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Why VXV and VIX Futures Do Not Create a Risk-Free Arbitrage

Article Quant Q&A · Author: Lisa Ann
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Summary

The document asks whether a short position in the three-month VXV index and a long position in a two-month VIX future can lock in a volatility spread. The proposed reasoning is that both positions might converge to VIX exposure at the future’s expiration, although they reference different volatility measures and tenors.

The answer highlights the key market constraint: VXV is an index rather than a tradable instrument, and the document says there are no VXV futures. Since the index itself cannot be bought or sold, the proposed short leg cannot be established directly, so the spread is not an executable arbitrage. The discussion does not analyze hedges that might approximate VXV exposure, transaction costs, or other practical strategies; its conclusion is limited to direct trading of the index.

Key ideas

  • VXV measures three-month volatility, while VIX futures are derivatives on VIX.
  • The proposed convergence argument does not make the two positions directly tradable equivalents.
  • The answer identifies VXV’s lack of tradability as the obstacle to the proposed arbitrage.

Tags

VolatilityFuturesArbitrage
Full text
# VXV vs. VIX futures: arbitrage opportunities?


# VXV vs. VIX futures: arbitrage opportunities?












At a first glance, VXV and VIX futures should not be compared at all: VXV is an underlying index, whilst VIX futures are derivatives written on a different underlying index, that is, VIX.

As instance, from a fixed income point of view, using VIX futures to seek opportunities on VXV seems like using EURIBOR 3M IRS to seek opportunities on EURIBOR 6M spot price: complete nonsense.

However, there's a point I am missing which puzzles me.

Follow my way of thinking:

- if I buy 2M VIX futures, two months later my contract will expire and converge to VIX spot price;

- if I replicate a VXV spot exposure through a carefully strike weighted straddle (see very famous More Than You Ever Wanted To Know About Volatility Swaps by Goldman Sachs' guys), two months later my exposure will converge to a VIX exposure, because my strike weighted options chain is not anymore centered on 3M tenor but on 1M ~ 30D tenor.

Therefore I have two positions which deliver the same payoff at some point: no-arbitrage rules would say that they should price the same, which is not true.

VXV vs. generic 2nd CBOE VIX futures spread:

If VXV is worth 22.5 and VIX 2M futures is slightly above 20.5, could you explain why shorting VXV and long such futures would not return me $2$ points of risk free volatility earnings?

## Answer by onlyvix.blogspot.com (score 3)

https://quant.stackexchange.com/a/24892

VXV is a 3-month volatility index, and is currently not tradable (there are no futures on it). And since you cannot trade it, you cannot arb it.

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.