Do the same or similar comparison with american put options to derive the boundary conditions for put options. Please also explain the logic behind.

Boundary Conditions for Options Compare two ways to buy a stock so that you own it at time T: Cash-Flow now A. Buy the stock now - St B. Buy a call option and deposit PV(X) - Ct - X/(1+r) Value at T ST MAX(ST-X, 0) +X Value of strategy B at time T: ST-X+X = ST if ST> X (i.e. the same as for strategy A). X when ST A => B must now cost > than A => Ct+X/(1 + r) 2 St (and since Ct20) => Ct > MAX (St - X/(1+r), 0) => A boundary condition! Boundary Conditions for Options Compare two ways to buy a stock so that you own it at time T: Cash-Flow now A. Buy the stock now - St B. Buy a call option and deposit PV(X) - Ct - X/(1+r) Value at T ST MAX(ST-X, 0) +X Value of strategy B at time T: ST-X+X = ST if ST> X (i.e. the same as for strategy A). X when ST A => B must now cost > than A => Ct+X/(1 + r) 2 St (and since Ct20) => Ct > MAX (St - X/(1+r), 0) => A boundary condition