Oh, I see - when you said "time value" you look at it vs spot, not the forward. I would describe this situation as "the put is pricing below the intrinsic value vs the forward". In short, you are saying that someone has mis-priced the forward which should never happen in the modern world.Here's an example of a mispricing:
XYZ is $40
Nov $45 put is $5.30
Dividend is is 50 cts.
Buy stock/buy put, exercise the next day after ex-div
- $40.00 - $5.30 + $45.00 + $.50 = + 20 cents