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Time value of European options
Why can the time value of an European put option be negative whereas the time value of an European call is always positive (assuming no dividend is paid).
Time value of European options
In words, it is because early exercise of a call means that you pay the strike early, losing out on value, while early exercise of a put means you get the strike early, gaining value.Mathematically, recall that the time value of a call less the time value of a put = c-p - S + KHowever, put call parity has the extra discounting.c-p=S-Ke^{-rt}So, time value of call less time value of a put = c-p-S+K = S-Ke^{-rt} - S + K = K(1-e^{-rt})or, the time value of a put = time value of a call - K(1-e^{-rt})so, if K(1-e^{-rt}) is large, the time values can differ signficantly.