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5

With a long time to maturity, your options have a low theta because their time value decays quite slowly. If there are many months to go, the passage of one day does not change the exercise probabilities too much, whereas short life options with only a few days left have a much higher time value decay. Hence, the larger the time to maturity, the lower theta. ...

4

This is possible if the option is long-dated and interest rates are high enough. For example, a five-year put struck at \$90 where the spot is \$100 (so it is in the money with respect to the spot price) with implied volatility 20% and interest rates 10% has a theta of \\$0.19.

3

That is quite possible. You have negative time value and a positive theta if the option price is below the intrinsic value. Look at deep ITM put options, the stock price is basically so low, the chance of it rising is negligible and the option price is the discounted payoff. This has a positive theta since the longer the time of maturity, the lower the ...

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