(c) Consider a European put option with strike price K and expiry time T. The underlying share does not pay any dividends during the lifetime of the option. Suppose that, at some earlier time t, the market price of the option is Pt, and the market price of the share is St > 0. The continuously-compounded risk-free interest rate is r. Show that Pt must satisfy each of the following conditions, otherwise there will be arbitrage opportunities: [4] (i) Pt > 0. (ii) Pt Ke-r(T-t) St. [4] Hint: For each case separately, identify an arbitrage opportunity if the condition does not hold. (c) Consider a European put option with strike price K and expiry time T. The underlying share does not pay any dividends during the lifetime of the option. Suppose that, at some earlier time t, the market price of the option is Pt, and the market price of the share is St > 0. The continuously-compounded risk-free interest rate is r. Show that Pt must satisfy each of the following conditions, otherwise there will be arbitrage opportunities: [4] (i) Pt > 0. (ii) Pt Ke-r(T-t) St. [4] Hint: For each case separately, identify an arbitrage opportunity if the condition does not hold