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Estimating Historical ATM Option Prices from Volatility Indices

Article Quant Q&A · Author: Terco
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Summary

The document asks how to estimate historical at-the-money S&P 500 option prices using public data, including VIX or another implied-volatility index, and whether modestly out-of-the-money strikes could also be considered. The answer points to a published paper that describes a procedure for calculating ATM option prices using a public volatility index as the volatility input.

The response specifically recommends consulting the paper’s indicated pages for the method, but it does not reproduce the pricing steps, assumptions, or required inputs. It therefore gives a useful source for further study rather than a complete recipe. The exchange does not establish that VIX can be substituted directly for implied volatility at every strike or maturity, nor does it explain how to price the proposed out-of-the-money options.

Key ideas

  • Public implied-volatility indices can provide a volatility input for estimating historical ATM option prices.
  • The answer directs readers to a paper describing such a procedure.
  • The document does not provide the actual pricing formula or implementation details.
  • It leaves unresolved whether an index volatility applies directly to other strikes and maturities.

Tags

OptionsVolatilityDerivatives pricing
Full text
# Calculate historical (ATM) option prices with public data


# Calculate historical (ATM) option prices with public data












I just saw the question How to calculate the most realistic historical option prices with additional publicly available parameters and I am interested in the step before that.

How can I calculate historical ATM option prices for the SP500 using VIX prices and other publicly available data? Can I just use VIX as implied volatility? can I go slightly out of the money (to 2% or 5%)?

Any links to examples or code will be appreciated!

## Answer by vonjd (score 2, accepted)

https://quant.stackexchange.com/a/3713

I don't know if I understand your question correctly but the procedure how to calculate ATM option prices with publicly available implied volatility indices (like VXO) for the vol parameter can be found in the mentioned paper on pages 5-7:

How Students Can Backtest Madoff’s Claims by Michael J. Stutzer (2009)

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.