# In this scenario could gamma be higher for OTM options?

Let's say there is a $1 stock, with say 1 day to expiration. The 1.5 strike call, is probably a 0 delta at this point; however, a 1 point increase would mean the stock would be at trading at 2 dollars; thus the 1.5 strike call would now almost be guaranteed to finish in the money right, and would seemingly now have close to a 100 delta. It seems then, that it's gamma was 100 in this scenario, making it higher than an ATM option. Where am I wrong? ## 1 Answer under the black scholes assumptions it is nearly impossible to move 50% in 1 day. A 1day move will be of size$\sigma \sqrt{1/252}$(assuming 252 trading days). So you are talking about something that is about a 40 stdev move (assuming$\sigma\$ = 0.2).

that's why your gamma is 0.