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Interpreting ATM Volatility and Implied Volatility Smiles

Article Quant Q&A · Author: glork
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Summary

The note explains why a chart might show an implied volatility curve and a flat volatility curve crossing at the at-the-money point. The crossing follows from how the illustration was constructed: the two example curves were chosen to have the same ATM volatility. One curve has negative skew, a pattern often associated with equity markets, while the other is flat.

The answer cautions that this visual relationship is not a general rule about volatility curves. The flat curve serves as a simplified comparison and is described as uncommon in observed markets, though consistent with the theoretical pattern associated with Black–Scholes. The document provides no data or empirical test; it clarifies only the illustrative choices behind a particular diagram. Readers should therefore avoid inferring that implied volatility curves must cross a flat curve at ATM in market data, or that every market has the same skew.

Key ideas

  • A displayed crossing at ATM can result from choosing curves with the same ATM volatility.
  • The example contrasts a negatively skewed implied volatility smile with a flat curve.
  • A flat volatility curve is presented as a theoretical simplification rather than a typical observed market pattern.
  • The diagram illustrates one choice and does not establish a universal rule.

Tags

OptionsVolatilityDerivatives pricing
Full text
# ATM volatility and flat volatility


# ATM volatility and flat volatility












Why do the implied volatility curve and the flat curve cross over the ATM volatility (at 100%) ?

Tx

## Answer by Quantuple (score 1, accepted)

https://quant.stackexchange.com/a/25828

Well... this is simply a picture to illustrate what is written in the text. It is not an absolute truth.

The author just chose 2 implied volatility smiles that share the same ATM volatility level for clarity. One exhibits negative skew (typical of equity markets) and the other one is flat (you'll never observe that in practice, although it is exactly what the theoretical Black-Scholes tends to predict).

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.