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How VIX Futures Converge Through Cash Settlement

Article Quant Q&A · Author: user61297
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Summary

The note explains why VIX futures can converge toward the published spot VIX near expiration even though the spot index itself is not tradable. Futures settle in cash, with the settlement amount determined on delivery day from a calculation closely related to the VIX formula. That calculation uses S&P option prices, with adjustments intended to exclude options that cannot be traded.

As expiration approaches, the live VIX serves as an estimate of the value that will be used for settlement, giving futures a reference to converge toward. The response also points out that options markets provide a way to trade and arbitrage exposures linked to the settlement calculation. This is a concise explanation of the settlement mechanism, rather than a detailed derivation or empirical study; the exact settlement calculation differs slightly from the continuously published index.

Key ideas

  • VIX futures settle in cash based on a volatility calculation made on delivery day.
  • The settlement calculation closely follows the VIX methodology and uses S&P option prices.
  • The live VIX provides an estimate of the eventual settlement value as expiration nears.
  • Options markets provide a route for trading exposures related to the settlement calculation.
  • Small differences between the settlement calculation and the live index can affect convergence.

Tags

FuturesOptionsVolatilityArbitrage
Full text
# Why do VIX spot and futures converge if there is no cash and carry arbitrage?


# Why do VIX spot and futures converge if there is no cash and carry arbitrage?












Since VIX spot is not tradable, why do the futures and spot converge @ expiration? By what mechanism does this occur if arbitrage is not one of them?

## Answer by nbbo2 (score 1)

https://quant.stackexchange.com/a/70385

The futures deliver cash, but the amount of cash is calculated at 8:30am Chicago time on the delivery day using a formula that is almost identical to the VIX formula. (There are minor differences to better exclude untradeable options from the calculation). So basically you receive "the value of the VIX at 8:30" on the delivery day. Of course in the minutes (and days) before this the futures converge to the live VIX, which is constantly recalculated and published by the CBOE, it is a reasonable estimate of what the 8:30 calculation will yield. And arbitrage via the options market can take place, since the formula is based on S&P option prices.

You can read in more detail here under Product and Settlement information

https://www.cboe.com/tradable_products/vix/faqs/

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.