VIX Measures Versus At-the-Money Option Implied Volatility

Summary

The document asks how the VIX or its short-term counterpart compares with implied volatility backed out from a near-the-money S&P 500 call. The response highlights that a Black–Scholes implied-volatility estimate is conditional on the model used to translate option prices into volatility. Its assumptions include a risk-neutral pricing framework and a specified return distribution, so the resulting estimate is not simply a direct observation of future realized volatility.

The answer contrasts this with VIX methodology, which aggregates a range of option prices through a model-free variance calculation rather than inferring volatility from one at-the-money call under Black–Scholes. That distinction can make the measures differ, but the document provides no historical comparison, empirical rule of thumb, or evidence for how large or stable any gap is. “Model-free” should also be understood relative to a specific option-pricing model, not as assumption-free: the index still depends on option-market prices, contract selection, and its calculation conventions.

Key ideas

• A Black–Scholes implied-volatility estimate depends on the model assumptions used to invert an option price.
• The VIX calculation aggregates a range of S&P 500 option prices instead of relying on one at-the-money call.
• Differences between the measures are possible, but the document gives no historical estimate of their typical size.
• The term model-free describes the VIX calculation relative to a specific option-pricing model, not an absence of assumptions.

Tags

# Difference between VIX9D and IV of 7 days near the money calls on S&P500


# Difference between VIX9D and IV of 7 days near the money calls on S&P500












What is the difference between VIX9D and IV of 7 days near the money calls on S&P500? (Or the VIX and 30day calls)

I was wondering if there is a thumb rule about this.

Looking at the current SPX options chain it seems to me to be about fluctuating between 2-3% but I couldn't find available historical data to show that this is true historically or in more volatile market times.

## Answer by KaiSqDist (score 0)

https://quant.stackexchange.com/a/81210

Using ATM 30D call option to backout the IV (that is the expected 30D volatility) via Black-Scholes forces you to incorporate the implicit risk-neutral assumption (and others, such as normality of log returns), which may not be reflective of the real world.

The VIX uses a "model-free" non-parametric method to compute the expected 30D volatility. Therefore, there are no assumptions made when computing this measure, and may be more accurate.

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.