As option nears maturity, what happens to value of theta?
I did a quick plot in Excel: as time to expiry declines from 1 year to zero, theta changed from -0.4950 to -0.4975.
I think it’s safe to say that it remains pretty close to constant.
From Exam perspective:
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Option value is negatively related with Theta (Time decay). As you move forward, closer to the maturity, option value declines for both call and put option (with some exceptions).
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Think about : if the option is out of the money, there is less time for it to go back in the money.
Hope it helps.
Theta increases for ATM decreases for OTM as time to expiry falls.
Theta and Gamma are the flipsides of the same coin - you are paying for that convexity in theta. The only position which is long gamma and positive theta is a deep ITM European put which can trade below intrinsic given high enough rates.