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.

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.

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.