Hi, suppose that current delta is 0.5 and that I want to know how much should the underlying move approximately in order for the delta to move to 0.6. I know this will depend on many variables, including implied volatility, but is there a quick rule of thumb I can use to get this info based on some assumptions, just to have a rough estimate?

Add the absolute value of the difference between the .50 and .60 delta strikes to the current price of the underlying. Very rough estimate when you need to pull a stop or tp from thin air, fast.

Thanks, that's a good suggestion. But what if I don't have access to the chain? I only know that my option is now delta 0.5 and want to put an alert when the market moves X points cause I expect that my new delta would be approx 0.6 at that point.

Well, the chain is probably the bare minimum you should have access to. If you only have access to the greeks for your option at the time, then approximate with gamma. Do consider that if the option price sensitivity is too high for your ability to access timely pricing, you may be better off zooming out of the action, play for a larger magnitude move with a longer term expiration. You will have more than enough time to model price and volatility scenarios with Sunday morning coffee. Slow the game down to your pace.

Take a look at GME. This Friday it’s $5 between .50 and .60. Two years out it’s $80. How can you make a rule of thumb with this much difference?

Within the same expiration only. Preferably near term. Over time, even minute differences in the vol surface will have a bigger impact on the premium.

My apologies for misunderstanding. Perhaps, the OP can give more information on how long he expects this move to take. I going by intra day changes these days.

Well I guess that assuming the move will realize over a longer period of time will add complications given delta will decay as well. So I was thinking a situation like this: each day I know my basic greeks and I want to be notified when the underlying reaches a point where my delta hits a given threshold. I can divide the difference between my threshold delta and the current delta by the gamma to get the points move in the underlying. So for example a SPY call with delta 0.5 and expiring mid Oct has now a gamma of 0.03, so the delta will increase by this amount for each point SPY increases. If my threshold is delta 0.6 I divide 0.1 by 0.03 to get a 3.3 move in SPY that would make my new delta 0.6. I was just wondering if there is a simpler way of doing that.

The gamma change on that expiry will be rapid ATM. Within a 2 week expiry is a significant amount of theta eroding prem. as well, much less relevant if you are looking at a 2 week change from day 360 to day 345. Farther out, you have deal with more vega. I find it hard to see how such a high amount of imprecision can be useful or actionable.