V. (14 points) Answer the following questions. a. (6 points) On the expiration date, the spot price of an asset is Sy. Consider a put option on the asset, with option premium, Pp and strike price K. Use a mathematical equation to express the profits of a buyer and a writer of one such put option as a function of St. Pp, and K b. (2 points) Consider the same asset and put option in part a), Use a mathematical equation of express the profits of a buyer and a writer of "n" units of such put option as a function of Sy, Pp, and K, and n. c. (6 points) On a 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, and the profit as the vertical axis. Label your curves clearly. Portfolio (1): buy (long) one call option with strike price of $10, option premium of 8; Portfolio (2): buy (long) one call with strike price of $30, option premium of $4; Portfolio (3): write (short) 2 call options with strike price of $20, option premium of $4.5. Also, draw the combined profit of Portfolio (1). (2), and (3) above. V. (14 points) Answer the following questions. a. (6 points) On the expiration date, the spot price of an asset is Sy. Consider a put option on the asset, with option premium, Pp and strike price K. Use a mathematical equation to express the profits of a buyer and a writer of one such put option as a function of St. Pp, and K b. (2 points) Consider the same asset and put option in part a), Use a mathematical equation of express the profits of a buyer and a writer of "n" units of such put option as a function of Sy, Pp, and K, and n. c. (6 points) On a 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, and the profit as the vertical axis. Label your curves clearly. Portfolio (1): buy (long) one call option with strike price of $10, option premium of 8; Portfolio (2): buy (long) one call with strike price of $30, option premium of $4; Portfolio (3): write (short) 2 call options with strike price of $20, option premium of $4.5. Also, draw the combined profit of Portfolio (1). (2), and (3) above