A European call option for a stock has an exercise price of $70, and expires one year from today. Suppose that the stock price has an equal probability of being valued at $60, $70, $75, $83, and $89 dollars per share, one year from now. What is the current present value of the option, given an effective annual rate of 10%

Find attached complete question with multiple choices:

The correct option is E,$6.7

Explanation:

The current present value of the option given an effective annual rate of 10%  is the sum of payoffs from different stock prices discounted to present value as below:

Payoff is potential gain from buying the share in a year's time at the exercise price of $70

    Stock price        option  price    payoff

     $60                     $70                 $0

    $70                       $70                 $0

    $75                        $70                 $5

     $83                       $70                 $13

     $89                        $70                $19

Total payoffs=$0+$0+$5+$13+$19=$37

Average payoff(there are 5 different possible prices)=$37/5=$7.4

Present value of average payoff=$7.4/(1+10%)^1=$ 6.73  

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