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ps5solutions - BAYLOR UNIVERSITY HANKAMER SCHOOL OF...

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1 B AYLOR U NIVERSITY H ANKAMER S CHOOL OF B USINESS D EPARTMENT OF F INANCE , I NSURANCE & R EAL E STATE Dr. Garven Name __SOLUTIONS___ Problem Set #5 (extra credit) 1. The price of a share of ABC stock is currently $50. It is known that at the end of 1 year, the ABC share price will be either $100 or $25. The riskless interest rate is 4% per year. Using the delta hedging, risk neutral valuation, and replicating portfolio approaches, calculate the price of a European call option on ABC stock with an exercise price of $40 that expires 1 year from today. Delta Hedging Approach : At the end of 1 year, the value of the call option will be either $60 (if the stock price is $100) or $0 (if the stock price is $25). Consider a portfolio consisting of shares and -1 call option. Then the value of the portfolio will be either 25 or 100 - 60 in 1 year. If we select such that the portfolio is perfectly hedged, then 25 = 100 - 60, = 0.80, and the value of the portfolio will be $20 with complete certainty. The current value of the riskless hedge portfolio is 0.80 x $50 c , where c represents the value of the call option. Since the portfolio must earn the riskless rate of interest, we can solve for c by determining the future value of 0.80 x $50 c and equating this with the $20 certain future value of our portfolio: (0.80 x $50 c ) e . .04 = $20 $40 - $20 e -.04 = c c = $40 $19.22 = $20.78 Consequently, the value of this call option is $20.78.
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