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CHAPTER_21 - CHAPTER 21 Valuing Options Answers to Problem...

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1 CHAPTER 21 Valuing Options Answers to Problem Sets 1. a. Using risk-neutral method, ( p X 20) + (1 - p )(-16.7) = 1, p = .48. Value of call = ( ) ( ) 8 . 3 01 . 1 0 52 . 8 48 . = × + × b . Delta = = 544 . 7 . 14 8 = c. d. Possible stock prices with call option prices in parentheses:

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2 e. Delta = = 544 . 7 . 14 8 = 2. (a) No. The maximum delta is 1.0 when the ratio of stock price to exercise price is very high. (b) No. (c) Delta increases. (d) Delta increases. 3. Using the replicating-portfolio method: a. If month 3 stock price = 350.85, delta = (30 – 0)/(430-286.27) = .209 To replicate call, buy .209 shares, and borrow PV(59.752) Option value = .209 X 350.85 – 59.752/1.0075 = 13.93 b. If month 3 stock price = 527, delta = (245.90 – 30)/(645.90 – 430) = 1 To replicate call, buy 1 share, and borrow PV(527) Option value = 1 X 527 – 400/1.0075 = 129.98 c. At month 0 delta = (129.98 – 13.93)/(527 – 350.85) = .659 To replicate call, buy .659 shares, and borrow PV(217.29) Option value = .659 X 430 – 217.29/1.0075 = 67.7 Using the risk-neutral method: p X .2269 + (1 – p) X .184 = 0.0075: p = .4671 a. If month 3 stock price = 350.85
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CHAPTER_21 - CHAPTER 21 Valuing Options Answers to Problem...

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