Valuation / pricing of options

Hey guys!

I have a doubt in options pricing, which goes as follows:-

Disclaimer - This is not any infringement of the CFA guidelines.

Source: CFA module Pg. 127 - Derivatives

Determine the payoff of the following strategies:

Problem F - The underlying is a stock priced at 40. A call oprtion with an exercise price of 40 is selling at 7. you buy stock and sell the call. At expiration, stock price is :

A. 52,… B. 38

My Solution: - logically, at 52, call would be exercised at 40, and the benefit goes to the call buyer. He paid 7 as option price, and he exercises the option at 40, when the price is 52, a payoff of 12. Net profit = 12-7=5

And the seller of the option gains 5 only (as he would have to sell the stock to buyer for 40, and bought at 40. => gain = 0.

However, the module has the following answers - A.40, B 38. with the explanation that ‘for any value at or above 40, the payoff is constant at 40’ With any decline in stock price below 40, the payoff declines. Ok.

So, is not the option value = intrinsic value + time value. However, at expiration, time value = 0.

Moreover, we are talking about payoff, so, how can the answer not be what I have calculated?

And is not the option price = option value?

Huff! Lot of questions… Please take time and respond…

As you say: they’re asking for the payoff, not the profit. By “payoff”, they mean the cash flow at expiration/exercise.

You’re correct in your calculation of the profit.

Hey! the same problem struck! But now I got your point. I think my calculation of profit is not correct though. As he sells the call, his income is the option premium / price = 7. The buyer of the call will make the profit of (52-40)-7=5. It is the other way!.. :stuck_out_tongue: