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Why Autocallables Depend on Volatility of Volatility and Forward Smile

Article Quant Q&A · Author: Pira
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Summary

The document raises a pricing question about autocallable products: why their value can depend on volatility of volatility and the forward smile, and why a local stochastic volatility model may be appropriate. The questioner offers a hedging intuition for forward-smile dependence: an autocall can terminate the product early, requiring a vega hedge to be reduced at a later date when the option smile may have changed.

The source provides no answer, derivation, references, or market evidence about the size or direction of these effects. Its hedging explanation is a starting intuition rather than a complete valuation argument, and it does not explain volatility-of-volatility in detail. The document therefore identifies relevant modeling considerations but leaves the requested explanation and justification for local stochastic volatility unresolved.

Key ideas

  • An autocallable’s early termination can require a trader to unwind part of a vega hedge.
  • The forward smile at the unwind date may differ from the smile used when the hedge was established.
  • The question asks why volatility of volatility matters and whether it supports using a local stochastic volatility model.
  • The document offers no derivation or evidence that quantifies these pricing effects.

Tags

OptionsVolatilityDerivatives pricing
Full text
# Why is an Autocallable dependent on the vol-of-vol and forward smile?


# Why is an Autocallable dependent on the vol-of-vol and forward smile?












I am trying to build an intuition on why an Autocallable is dependent on the vol-of-vol and forward smile, justifying why we should use LSV model. I have a simple intuition for the latter: I am initially long vega so if AC event I have to buy-back some vega to unwind the vega hedge. For exemple in case of a 3Y AC, if in 1 year there is an autocall event I have to unwind some vega on a smile that is different (for the same options). So it makes the AC more expensive using LSV compared to LV.

Can you please refer me to some paper/books to get a better intuition, especially on the vol-of-vol or explain it clearly?

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