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Why the VIX Forward Price Formula Uses SPX Options

Article Quant Q&A · Author: MikeD
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Summary

The document asks why the VIX calculation’s forward index price formula appears not to account for dividends, given that the S&P 500 constituents pay them. The concern comes from comparing the formula with a general put-call parity expression that uses a discount factor incorporating rates and dividends. The answer resolves the apparent mismatch by distinguishing the index from its component stocks: VIX is calculated from SPX index options, and SPX itself does not pay dividends.

This is a concise conceptual clarification rather than a derivation of the VIX methodology. It does not explain the full forward-price calculation, the dividend treatment in pricing constituent stocks or other index products, or whether conventions can change across settings. Its main lesson is to identify the underlying instrument correctly before importing assumptions about cash distributions from the securities it represents.

Key ideas

  • VIX uses SPX index options as its inputs.
  • SPX itself does not make dividend payments, even though its constituent stocks may.
  • The answer attributes the apparent dividend mismatch to confusing the index with its constituents.
  • The response offers a brief clarification rather than a full derivation of VIX methodology.

Tags

OptionsVolatilityDerivatives pricingUS markets
Full text
# Forward Index Level in VIX calculation


# Forward Index Level in VIX calculation












The VIX white paper (https://cdn.cboe.com/resources/vix/vixwhite.pdf) step #1 (page 6) says the the Forward Index Price is calculated as:

F = Strike Price + e^RT x (Call Price - Put Price).

Why doesn't it take dividends into account? Many of the S&P 500 stocks pay dividends, so isn't this formula going to over-estimate the forward index level?

I thought forward price is calculated using put-call parity:

```
C - P = D(F - K).

C: call price for strike K
P: put price for strike K
D: Discount factor (takes dividends and interest rates into account)
F: forward price
K: strike
```

The VIX seems to ignore the dividends portion of the discount factor.

## Answer by Peter Zerg (score -1)

https://quant.stackexchange.com/a/73439

SPX does not pay dividends, and VIX is based on SPX 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.