# Question on principals of option pricing

Book: Derivatives and Alternative Investments Page: 101 Questions: F and G Hi guys, I am having a tough time understanding the logic behind the answers for these two questions. Could you please help clarify it? The link will take you to the pic of the questions.

http://i644.photobucket.com/albums/uu164/hieracity/CFA/derivatives_pg101.png

Thank you!

Fi. You buy the stock (-\$40) and sell the call (+\$7) = “covered call”. At expiration the call is exercised at \$40 so the person pays you \$40 and you give them the stock you bought. As long as the stock price > the strike the stock price isn’t relevant to your cash flow. The stock could be \$152 and your cash flow would still be the same. Gi. you buy the stock (-\$60) and buy the put (-\$5) = “protective put”, so your current cash flow is -\$65. at expiration the stock is worth \$68, so you sell the stock for \$68. The put expires worthless because the stock isn’t lower than the exercise price. You net cash flow is -\$65 + \$68 = \$3.

If you need to understand American Put Options. You can access the link for Video Tutorial. http://www.thecfaexperience.com/2011/12/american-put-options.html

It might speed you up if you learn to express your positions the way the book suggests. Specifically, whenever you buy/go long something, you enter it with a “+”. If you’re selling/going short you enter it with a “-”. For stocks you just enter its price; for options the respective payoff (max(0, S-X) for calls; max(0, X-S) for puts), and for bonds just par value (usually X), sometimes discounted. In F.i, you have bought the stock and shorted the call. So your position is worth: +52 - max(0, 52-40) = 40 In F.ii you have the exact same position, but a different price of underlying. +38 - max(0, 38-40) = 38 In G.i, you have bought the stock and bought the put. So your position is worth: +68 + max(0, 60-68) = 68 In G.ii you have the same position with a difference stock price. It is worth: +50 + max(0, 60-50) = 60

Is the best answer. Basically, cover the part where you are buying a stock (at the latest market price) and add/subtract to that the price of the option you are buying/selling. Call options should be priced as Max(0,S-X) and Put options should be priced as Max(0, X-S) where S is the value of the asset (in this case, stock) and X is the exercise price.