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Choosing Delta Rehedging Thresholds for a Positive Gamma Options Portfolio

Article Quant Q&A · Author: pavybez
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Summary

The document asks how to choose a delta threshold for rehedging a BTC options portfolio built to have positive gamma and negative initial cost. The portfolio is first made delta neutral, then the trader considers rebalancing after spot moves by a set percentage. Passive limit orders and exchange rebates are described as reasons transaction costs are not the main concern in this example.

The answer offers no universal threshold. It suggests simulating spot paths and assessing the losses from discrete hedging, which can remain even when transaction costs are absent. The trader can then choose a hedge trigger based on the amount of that risk they are willing to accept. The response does not provide a simulation design, a loss formula, or a threshold calibrated to the portfolio. Results will depend on the options, market dynamics, and the trader’s risk tolerance, so the suggested approach requires further modeling.

Key ideas

  • A positive gamma portfolio can be delta neutral at inception and still need rehedging as spot moves.
  • A fixed percentage trigger has no universally suitable value in the discussion.
  • Discrete delta hedging can incur losses even when transaction costs are ignored.
  • Simulating spot paths can help assess hedge losses and select a trigger consistent with risk tolerance.

Tags

OptionsCryptoVolatilityRisk management
Full text
# At what threshold on delta percentage should I hedge my option portfolio?


# At what threshold on delta percentage should I hedge my option portfolio?












I am able to identify and build an option portfolio with long/short call/put options across different strikes and expiries such that the gamma is positive and cost is negative. Upon inception I hedge the option portfolio so that delta is zero.

However, I am unable to identify at what threshold of delta% should I continuously hedge my portfolio as spot changes to keep it delta neutral. I set different thresholds such a 1%, 2%, 5% but not satisfied with this approach and was wondering if there is a more sound method.

Please not that transaction costs are not an issue. This is because the options are on BTC on Deribit exchange and since I start with a positive gamma (i.e. buy low sell high for delta hedge), I use passive LIMIT orders that have negative fees or rebates when filled.

For reference here is the github link

## Answer by KaiSqDist (score 0, accepted)

https://quant.stackexchange.com/a/76697

I seem to recall that delta hedging is not a perfect hedge, meaning that even if you do it discretely (and at a high frequency), there will always be losses (not transaction costs) in the process. These losses should be what you are focusing on. You could probably run some simulations (over an interval as to how the spot price changes) and test what amount of losses you are comfortable with before deciding what is the appropriate delta level you want to hedge at.

Hopefully this helps!

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