4. (a) (i) Explain carefully the difference between selling a put option and buying a call option. Write down the two payoffs and draw their graphs. [3] (ii) An investor buys one put option contract on the stock with a strike price of $20 and sells a put option contract on the stock with a strike price of $18.50. The market prices of the options are $2.50 and $1.75, respectively. The options have the same maturity date. Describe the investor's posi- tion and the possible gain/loss he will get (taking into account the initial investment). Make a graph of your gain/loss. [5] (b) (i) State the non-arbitrage principle. [1] (ii) State the put-call parity for both European and American options. (Clearly specify any notation that you use). (iii) Prove the put-call parity for European options. (1)