) Let V (S) = PBS(S) max(K S, 0) be the premium of the value of a European put option

on a nondividendpaying asset over its intrinsic value max(K S, 0), where PBS(S) is the

BlackScholes value of the plain vanilla European put option with strike K and spot price

S.

(i) Show that the maximum value of V (S) is obtained at the money, i.e., for S = K.

(ii) What is the asymptotic behavior of V (S) as S 0?

(iii) Plot V (S) as a function of S