(i) Use formulas (4.5.23)-(4.5.25), (4.5.26), and (4.5.29) to determine the delta Px(t,x) , the gamma Pxx(t,x), and the theta Pt (t,x) of a European put.
(ii) Show that an agent hedging a short position in the put should have a short position in the underlying stock and a long position in the money market account.
(iii) Show that f(t, x) of (4.5.26) and p(t, x) satisfy the same Black-Scholes Merton partial differential equation ( 4.5.14) satisfied by c(t, x) .
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has limit zero.