# Fin 432 Test two

### 102 terms by mwrig040

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### JsTest 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%, what is the price of a call option on the stock that has an exercise price of 22 and that expires in one year, rounded to the nearest dollar? [Hint: Use daily compounding]

This solution uses the Portfolio Replication Method. The stock's range of payoffs in one year is \$27 - \$17 = \$10. At expiration, the option will be worth \$27 - \$22 = \$5 if the stock price is \$27, and zero if the stock price \$17. The range of payoffs for the stock option is \$5 - 0 = \$5. 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's payoff will be either \$13.5 or \$8.5. The portfolio's payoff will be \$13.5 - \$5 = \$8.5, or \$8.5 - 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

\$3.00

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9

all in FPL

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7.68

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