Sticky Strike and Sticky Delta Assumptions in Hedge Greeks

Summary

The document raises implementation questions about sticky-strike and sticky-delta assumptions in options hedging. These assumptions describe how implied volatility is treated as spot moves, and therefore affect the relationship between spot changes and option volatility. The author views this relationship as similar to using spot as a proxy hedge for vega and asks how that exposure interacts with a separate vega hedge.

The author also asks whether changing assumptions requires adjustments to vega and gamma as well as delta. No answer or calculation is included, so the text does not establish which Greek adjustments are correct or give an implementation procedure. It serves as a prompt to examine how volatility-surface dynamics affect hedge sensitivities; conclusions would require specifying the surface convention, option model, and risk-measure definitions.

Key ideas

• Sticky-strike and sticky-delta assumptions imply different volatility behavior as spot changes.
• The document asks how these assumptions affect delta hedging when spot and implied volatility co-move.
• It raises whether proxy vega exposure should be netted against a separate vega hedge.
• It also asks whether gamma should change along with delta under the chosen assumption.
• No answers or implementation method are provided.

Tags

# Sticky strike sticky delta implementation


# Sticky strike sticky delta implementation












I'm a clear on the differences between the two assumptions but a bit confused on the practical implementation.

1) The aim of choosing one of the two assumptions is to take into account the co-dynamic between the spot and the vol when delta hedging. As a result, it is similar to proxy vega hedge with spot. However, if we vega hedge, this proxy should be netted and as a result, delta hedge + vega hedge should be the same quantity independently from the initial assumption. Does that mean that we also need to modify the vega when choosing between one of the two assumptions?

2) I find a lot of information on how to modify the delta. Do we agree that we should also modify the gamma accordingly?

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