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# wk6 - Solutions Tutorial Week 6 Chapter 22 9 a u = e 0.24...

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Solutions – Tutorial Week 6 Chapter 22 9. a. 844 . 0 / 1 ; 185 . 1 5 . 0 24 . 0 = = = = u d e u \$45 \$53.33 \$37.98 \$63.19 \$45.01 \$45.01 \$32.06 887 . 0 / 1 ; 127 . 1 25 . 0 24 . 0 = = = = u d e u \$45 \$50.72 \$57.16 \$64.41 \$35.41 \$50.70 \$39.92 \$44.98 \$39.91 \$72.60 \$57.14 \$57.14 \$44.97 \$44.97 \$35.40 \$31.41 \$35.40 \$27.86

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b. 809 . 0 / 1 , 236 . 1 5 . 0 3 . 0 = = = = u d e u \$45 \$55.62 \$36.41 \$68.75 \$45.00 \$45.00 \$29.46 \$45 \$52.29 \$60.76 \$70.60 \$33.36 \$52.32 \$38.75 \$45.02 \$38.77 \$82.04 \$60.79 \$60.79 \$45.05 \$45.05 \$33.38 \$28.72 \$33.38 \$24.73 861 . 0 / 1 ; 162 . 1 25 . 0 3 . 0 = = = = u d e u
12. a. The possible prices of Buffelhead stock and the associated call option values (shown in parentheses) are: Let p equal the probability of a rise in the stock price. Then, if investors are risk-neutral: p (1.00) + (1 – p) × (–0.50) = 0.10 p = 0.4 If the stock price in month 6 is \$110, then the option will not be exercised so that it will be worth: [(0.4 × \$55) + (0.6 × \$0)]/1.10 = \$20 Similarly, if the stock price is \$440 in month 6, then, if it is exercised, it will be worth (\$440 - \$165) = \$275. If the option is not exercised, it will be worth: [(0.4 × \$715) + (0.6 × \$55)]/1.10 = \$290 Therefore, the call option will not be exercised, so that its value today is: [(0.4 × \$290) + (0.6 × \$20)]/1.10 = \$116.36 b. (i) If the price rises to \$440: (ii) If the price falls to \$110: c. The option delta is 1.0 when the call is certain to be exercised and is zero when it is certain not to be exercised.

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wk6 - Solutions Tutorial Week 6 Chapter 22 9 a u = e 0.24...

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