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# Answer on Other Management Question for John

Question #12661
4. The current price of a stock is $22, and at the end of one year its price will be either$27 or $17. The annual risk-free rate is 6.0%, based on daily compounding. A 1-year call option on the stock, with an exercise price of$22, is available. Based on the binominal model, what is the option&#039;s value?
a. $2.43 b.$2.70
c. $2.99 d.$3.29
e. $3.62 Expert's answer Answer is c ($ 2,99)The stock&rsquo;s range of payoffs in one year is $27 -$17 = $10. At expiration, the option will be worth$27 - $22 =$5 in case the stock price is $27, and zero if the stock price is$17.

The range of payoffs for the stock option is $5 &ndash; 0 =$5. We equalize the range to find the number of shares of stock:

Option range / Stock range = $5/$10 = 0.5

With 0.5 shares, the stock&rsquo;s payoff will be either $13.5 or$8.5. The portfolio&rsquo;s payoff will be $13.5 -$5 = $8.5, or$8.5 &ndash; 0 = $8.5. The present value of$8.5 at the daily compounded risk-free rate is: PV = $8.5 / (1+ (0.06/365))365 =$8.005.

The option price is the current value of the stock in the portfolio minus the PV of the payoff: V = 0.5($22) -$8.005 = \$3.00.

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