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Reading SPX Convexity Spread and Ratio from Variance Swap Volatility

Article Quant Q&A · Author: Trajan
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Summary

The document explains the interpretation of two volatility measures: the SPX convexity spread, defined as variance swap volatility minus at-the-money implied volatility, and the convexity ratio, defined as variance swap volatility divided by at-the-money implied volatility. Both compare a flat-volatility reference with a measure that reflects the broader implied-volatility surface.

The answer characterizes these measures as aggregate indicators of how skew and kurtosis affect total volatility relative to at-the-money volatility. The document gives no derivation, empirical examples, or guidance on how to use the measures in trading. Its explanation is therefore conceptual and brief; it does not establish how either indicator predicts market behavior or performs in a strategy.

Key ideas

  • The convexity spread subtracts at-the-money implied volatility from variance swap volatility.
  • The convexity ratio divides variance swap volatility by at-the-money implied volatility.
  • Both measures summarize differences between flat volatility and volatility reflecting skew and kurtosis.
  • The document provides no empirical evidence or trading rules for interpreting these indicators.

Tags

OptionsVolatilityDerivatives pricing
Full text
# SPX Convexity Spread


# SPX Convexity Spread












In this report on volatility from BNP Paribas,

https://globalmarkets.bnpparibas.com/r/Volatility_Express_20171128.pdf?t=BG3REXwMP3NZJRN7wY5Vt&stream=true

it states on Page 10 that the SPX Convexity Spread is defined by Varswap - ATM IV. How does this work??

Also why do we care about SPX Convexity Ratio (= Varswap/ATM IV)?

## Answer by onlyvix.blogspot.com (score 3, accepted)

https://quant.stackexchange.com/a/40196

You can think of both ( difference and ratio ) indicators as some aggregated measure of difference between flat vol (ATM vol) and "total vol" than includes skew and kurtosis effects.

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.