Why Spot–Volatility Correlation Matters for Autocall Pricing

Summary

The document explains why the relationship between the underlying price and future volatility can affect autocall valuation. Autocalls often include digital payoffs and barrier conditions, so their value depends on the chance that the underlying crosses a level. In a constant-volatility Black–Scholes setting, expected volatility does not vary with the current spot level. A stochastic-volatility model can represent a negative association between spot and volatility, changing those crossing probabilities.

The example describes an underlying below a barrier: higher expected volatility can raise the chance of an upward crossing and a favorable payoff. Above the barrier, the analogous chance of a downward crossing may matter differently. The discussion is qualitative and gives no pricing experiment or quantitative comparison. It raises questions about local-volatility and quanto products but does not answer them, so its explanation should not be treated as a complete account of their sensitivity to spot–volatility correlation.

Key ideas

• Autocalls often contain digital and barrier features whose values depend on level-crossing probabilities.
• In a constant-volatility model, volatility is independent of the current spot level.
• Stochastic volatility can model a negative association between spot and volatility.
• The impact of expected volatility on crossing chances can differ depending on the spot’s position relative to a barrier.

Tags

# Correlation Spot Vol - when is it important?


# Correlation Spot Vol - when is it important?












I know that a local volatility model does not allow to control the correlation between Spot and Vol. I know also that the correlation Spot Vol is important for products like autocalls. Why is correlation spot vol important for autocalls? In which cases the correlation spot vol is important? Is it important for quanto options?

EDIT

I saw this interesting answer: What are the advantages/disadvantages of these approaches to deal with volatility surface? What is the forward volatility? How can we see mathematially that the forwrd volatility of a local volatility model flattens out?

## Answer by bigInner (score 1)

https://quant.stackexchange.com/a/72059

When pricing autocalls you are basically dealing with digitals and barriers. The probability of crossing barrier/digit up or down is governed by how much volatility is expected in next spot moves. This expected volatility in BS model is constant regardless of your spot level now. On the other hand, the vol is negatively correlated with spot level in a stochastic vol model. e.g if spot is below the barrier, the expected vol is more important (you are more likely to cross the barrier up and become ITM) than if your are above the barrier (less likely to cross the barrier down and become OTM).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.