Collecting theta

nope, it decreases for both OTM and ITM

 

I'm afraid crgarcia's statement is correct.
As has already been stated, the atm has the highest theta while the away from the money thetas decrease. BUT the NEAR month theta is larger than the FAR month. Iow theta for the near month option is greater than the far month equivalent strike option, e.g an option with 10 days to expiry will have a higher theta than an option with 19 days to expiry. Just look at any option chain to verify this.
db

 

Afraid it’s not. Attached theta for OTM and ITM calls using Hoadley pricer, underlying stuck @ 100 (this is BS, binomial is similar).

Actually, when you consider theta a negative number then it does increase i.e. approach zero from below, but don’t tell me that’s what you had in mind.....

 

Actually, it depends on how far OTM/ITM the option is. As you can see, deep OTM/ITM Theta does decrease, but closer to ATM Theta increases. The curve gets more peaked.

 

Whoa, hold on a minute chaps! Let me get this straight. You are saying that an otm/itm option with one month to expiry has a LOWER THETA than an option with three months (or whatever) to expiry?! Come on, just look at any option matrix and you'll see that's nonsense. And looking at options that are far away from the money is meaningless since they have virtually no liquidity. Iow for all practical purposes theta increases the less time to expiry.
db

 

dboy, when I lower vol from 0.4 to 0.2 theta decreases from 90 days on (see pic). Yes these are far-out options, essence is that there is always a point nearing expiration where theta peaks. As MTE points out, exactly where depends on the variables.

But the premise of OP’s question is true: OTM (and ITM) theta drops in the final so-many days.