Get confused on two opposite views on theta vs IV

L

LucasX

Someone said when IV decreases, Theta will be higher, especially when it is approaching expiration, vice versa.

On the other hand, I tried to punch in some numbers in the simulator. The result is just the opposite. Also, I had been seeing theta chart supporting my observation.

The chart (Theta vs IV) looks odd if I think IV as how many days left. The lower IV is essentially same as less days to expiration(correct me if I am wrong), and obviously theta will be higher close to expiration in chart (Theta vs time). I can't find the common ground on those two charts.
 
If you think about it, it should become obvious that as IV goes up, so does theta.

Think of it this way. Today the slightly-out-of-the-money IBM 120 calls closed at 2.45 bid, an IV of about 20%, with 11 days to expiration. If IBM doesn't move between now and expiration, these calls will become worthless, losing all 2.45 in premium.

But if IV were, say, doubled to 40%, the 120 calls would also approximately double - to about 4.90. Now, if IBM didn't move between now and expiration, each call would lose 4.90.

So which has greater theta - the option that loses 2.45 in 11 days, or the one that loses 4.90 in 11 days?
 
More time value in premium so does in theta. I got to that point but never went further to think about what if nothing happens and then option expires worthless.

Also I was caught in my argument and don't know why my explanation doesn't work. Apparently I can't use IV equals time to expiration that simple in this case.
 
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