4. American Options (a) Explain clearly what an American option is. How is it related to the European option? (a) Consider an American put option. Let P(S,t) denotes the value of the European put option. Show that arbitrage exists if we assume that the value P(S,t) is less than its intrinsic value. So we have to impose the constraint: P(S,t)max(SE,0) (c) Explain as best as you can the term optimal exercise price associated with an American option