Past exam of the martingales and financial mathematics course of the University of Oxford / 2008 / B / 6 / i / a / Solution

The terminal put payoff obeys $0\le (K-S_T{)}^{+}\le K$. If the put cost more than the zero-coupon bond paying $K$, sell the put and buy that bond. Invest the strictly positive initial difference in the bank account. At maturity the bond covers every possible put liability and the extra investment remains positive. This arbitrage is excluded, so