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6

No because they are worthless in the first place. Theta is in dollar space and therefore, if something is worthless, it is hard for it to lose much more value. Think about it this way. When you are buying an option, you are really buying gamma from BS PDE. The cost of gamma is theta. Where is gamma highest? ATM


3

It's hard to be sure without seeing the inputs, but I'm guessing that the implied curve changes shape because the original curve does (which you can see from your output: except for the 1-year and 5-years points, the actual discounts are different). The reason the original curve changes is probably the different position of weekends or holidays (so that, ...


1

Disclaimer: I did not check your example, i.e., that "theta * 1 day" will predict a negative option price. Theta is the derivative with respect to time-to-maturity. It is the change of the option price with respect to an infinitessimal change in time and not with respect to a change of one day - even if the derivative is "scaled" towards a time scale having ...



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