Bounds on European and American puts (a) 5. Using put-call parity and bounds on a European call, or otherwise, prove that the price ofa European put on a stock paying nd max 0, KZ (t, T) - St) s Pk (t, T) s KZ (t, T) Prove that the price of an American put on the non-dividend paying stock satisfies max (o, K - S) 3 Pk (t, T)s K. (b) (c) Give an example to show that the American put can be worth more than the European put, that is, where immediate exercise of the American gives payout at time T strictly greater than the payout of the European. Hint Exercising early means the strike price K will be received early. Consider under which environments this will be preferable. Bounds on European and American puts (a) 5. Using put-call parity and bounds on a European call, or otherwise, prove that the price ofa European put on a stock paying nd max 0, KZ (t, T) - St) s Pk (t, T) s KZ (t, T) Prove that the price of an American put on the non-dividend paying stock satisfies max (o, K - S) 3 Pk (t, T)s K. (b) (c) Give an example to show that the American put can be worth more than the European put, that is, where immediate exercise of the American gives payout at time T strictly greater than the payout of the European. Hint Exercising early means the strike price K will be received early. Consider under which environments this will be preferable