Why Autocallable Delta Can Differ Across Volatility Models

Summary

The document raises a model risk question about hedging autocallable notes. It describes a reported case in which a bank used local volatility to price the notes and consequently estimated a larger-magnitude delta than it would under a stochastic volatility model. The account says the bank interpreted that estimate as a larger short exposure, bought too much stock to hedge, and suffered losses when the market fell.

The central question is why the delta difference might have that direction, given that the models also differ in price because stochastic volatility includes volatility of volatility. However, the document contains only the question and offers no explanation, model setup, calculations, or supporting evidence. It therefore highlights the potential consequences of model choice and hedge calibration without establishing a general relationship between local and stochastic volatility deltas. Conclusions would require product terms, market inputs, and a specified calibration and delta convention.

Key ideas

• The document reports that local volatility produced a larger-magnitude autocallable delta than stochastic volatility in a particular case.
• A hedge based on that estimate led to excess stock purchases, according to the account.
• The proposed explanation is unresolved in the document.
• Delta comparisons depend on the product, model calibration, and hedge convention.

Tags

# Autocallable option Delta


# Autocallable option Delta












There have been numerous exotic trading desk blow ups lately, related to various reasons. However, in particular, one bank had some issues where they were pricing autocallable notes with Local Volatility and not producing a Delta "true up" using Stochastic Volatility that is common among other banks. In other words, Delta of the autocallable notes is higher in magnitude under Local Volatility compared to Stochastic Volatility. Since the bank thought it was holding more (negative) Delta as a result of the Local Volatility model, they bought too much stock to hedge and had large losses when the market declined.

Can someone provide an intuitive explanation of why Delta is higher in autocallable products under Local Volatility compared to Stochastic Volatility? The price of the product is different under the two volatility models on account of vol-of-vol differences, but it's not entirely clear to me why the Delta difference is in this direction.

Thanks.

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