Solarcity Feb 2016 from 28 to 16 within one week
Twitter, also Feb 2016 from 13 to 18+
Aixtron, May 2016 from 3.80 to 5.70 within 3 days, main part was in a gap opening
Then there are numerous daily movers that move beyond 30%, and a fair few with options.
I've seen these moves on expiration days, mid-week... it's not uncommon.
The ones I mentioned I just remembered... didn't even run an analysis of daily/weekly movers. And those are not small low cap firms.
OP will look at highly volatile stocks for his strategy so he can sell high premium OTM's /strangles... so probably thinly traded stocks which will have these moves now and then... probably low market cap firms, which have higher takeover risk or bankruptcy risk... hence the high implied vols and high option premiums. He will run this strategy on multiple stocks per week... And he is looking at keeping the positions until expiry, only (trying) to hedge when it hits his short strike(s).
With the strategy he's looking at, that 50% move or more and probably even a 35% move will wipe his account out....
[edit]... I forgot my favorite, Nintendo... +85% within a few days after Pokemon Go came out, Then another 38 within another few days... then a 55% drop... And this is a USD 15 bln company when it started.
[edit 2]... Volkswagen Oct 2008 went from 170 to 1000 in a few days... and back to 'normal'...
[edit 3].. .damn, I keep editing because I keep remembering big ones... Volkswagen again from 160 to 100 with the diesel scam....