III. (20 points) Answer the following questions. a. (7 points) On the expiration date, the spot price of an asset is . Consider a put option on the one unit of the asset, with option premium, Pp, and strike price K. Use a mathematical equation to express the payoffs and profits (net payoffs) of a buyer and a writer of one unit of such put option as a function of , Pp, and K. Draw two 2 diagrams: on one diagram, draw the payoff of the buyer and the writer; on the other, the profits of the buyer and the writer. Note: the horizontal axis should be the spot price, . b. (5 points) Consider the same asset and put option in part a), Use a mathematical equation to express the profits of a buyer and a writer of "n" units of such put option as a function of , Pp, and K, and n. c. (8 points) On the same diagram, draw the profits of the following portfolios on the expiration date. Suppose all options have the same expiration date, and set the spot price of the asset as the horizontal axis. Label your curves clearly. Portfolio (1): buy (long) one call option with a strike price of $10, option premium of 8; Portfolio (2): buy (long) one call with a strike price of $30, option premium of $4; Portfolio (3): write (short) 2 call options with a strike price of $20, option premium of $4.5. Also, draw the combined profit of Portfolio (1), (2), and (3) above.