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How Spot–Volatility Dependence Relates to Volatility Smiles

Article Quant Q&A · Author: bigInner
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Summary

The document asks whether the volatility smile and the volatility-of-volatility smile can both arise from dependence between spot and volatility. It proposes viewing the relationship in two directions: volatility moves affecting spot may help explain the ordinary volatility smile, while spot moves affecting volatility may help explain the volatility-of-volatility smile. It also asks whether the same quadratic covariance underlies both effects.

No derivation, model, data, or answer is provided, so the proposed interpretation remains an open question rather than an established result. The note is useful as a prompt to distinguish dependence involving spot and volatility from the shapes of the two smiles, but it does not show that the effects are equivalent or identify conditions under which they would be. Readers would need a specified stochastic model and evidence to assess the conjecture.

Key ideas

  • The note asks whether spot–volatility dependence can explain both volatility smiles.
  • It conjectures that volatility moves affecting spot may relate to the ordinary volatility smile.
  • It proposes that spot moves affecting volatility may relate to the volatility-of-volatility smile.
  • It leaves open whether both effects arise from the same quadratic covariance.

Tags

OptionsVolatilityDerivatives pricing
Full text
# Volatility smile vs Vol of Vol smile


# Volatility smile vs Vol of Vol smile












Is the vol of vol smile due to the correlation spot/vol similarly to vol smile ? It seems that if we see the correl as the impact of vol on spot we get the vol smile. And if we see the same correl as an impact of spot on vol we get the vol of vol smile.

Concretely, a huge move in the vol contribute to the vol smile and huge move in the spot contribute to the vol of vol smile.

Are we talking about the same quadratic covariance here ?

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.