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

Question

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 1

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!