Under what conditions can a european option be worth as, Finance Basics

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Under what conditions can a european option be worth as

1. Under what conditions can a European option be worth as much as the equivalent American option?

2. Compare the direct value of exercising an American put that is in-themoney (you get K - S0) to the value of the put in the put-call parity formula P0(K) = C0(K) + [PV0(K) - S0 ] . Under what conditions is it better not to exercise the American put?

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