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How Option Hedges Change Volatility and Greek Exposure

Article Quant Q&A · Author: Nicolas
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Summary

The document compares delta hedging an options position with other options on the same underlying against hedging with the underlying asset. It explains that an underlying hedge offsets delta while leaving the position exposed to the underlying’s realized volatility. Using options as the hedge also introduces exposure to their implied volatility and can change the combined position’s gamma and vega, offering a way to manage more than delta.

The answers also identify access as a practical consideration: an underlying may be unavailable to trade even when options are accessible through an exchange or over the counter. The discussion is conceptual and brief; it gives no worked examples, pricing analysis, or evidence comparing hedge performance. The choice of hedge therefore depends on the desired exposures and market access, and the document does not offer a general rule for which approach is preferable.

Key ideas

  • Hedging delta with the underlying leaves exposure to realized volatility in the options position.
  • Using another option as a hedge adds exposure to that option’s implied volatility.
  • An option hedge can change the combined position’s gamma and vega as well as its delta.
  • Access to the underlying can affect which hedging instruments are practical.

Tags

OptionsVolatilityRisk management
Full text
# Delta re-hedging with options


# Delta re-hedging with options












What are the pros and cons of delta re-hedging an option combination (straddle, strangle etc...) with options of the same underlying rather than with the underlying itself? I am having a hard time finding litterature on the subject.

## Answer by Arshdeep (score 2)

https://quant.stackexchange.com/a/76157

Delta hedging with other options would give you exposure to the implied vol dynamics of those options. Delta hedging with the underlying gives you exposure to the realized volatility of the underlying.

It will also change the gamma/vega of your position which can be a significant improvement over just hedging with the underlying.

## Answer by Will Gu (score 1)

https://quant.stackexchange.com/a/31343

On top of my head, there are two reasons. One is that the underlying may not be accessible, while you can buy/sell options on exchange or OTC. The other (more important) reason is your position on other greeks (gamma, vega, etc). With appropriate options you can adjust both your delta and other greeks.

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.