answers-odd-problems-ch08

answers-odd-problems-ch08 - Equalize the range to find the...

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Chapter 8 Financial Options and Their Valuation SOLUTIONS TO END-OF-CHAPTER ODD NUMBERED PROBLEMS 8-1 P = $15; X = $15; t = 0.5; r RF = 0.06; σ 2 = 0.12; d 1 = 0.24495; d 2 = 0.0000; N(d 1 ) = 0.59675; N(d 2 ) = 0.500000; V = ? Using the Black-Scholes Option Pricing Model, you calculate the option’s value as: V = P[N(d 1 )] - t r RF Xe - [N(d 2 )] = $15(0.59675) - $15e (-0.10)(0.5) (0.50000) = $8.95128 - $15(0.9512)(0.50000) = $1.6729 $1.67. 8-3 . 3319 . 0 ) 33333 . 0 5 . 0 ) 333333 . 0 )]( 2 / 25 . 0 ( 05 . 0 [ ) 35 /$ 30 ($ ln t σ )]t 2 / 2 RF [r (P/X) ln 1 d - = + + = + + = d 2 = d 1 – s (t) 0.5 = -0.3319 – 0.5(0.33333) 0.5 = -0.6206. N(d 1 ) = 0.3700 (from Excel NORMSDIST function). N(d 2 ) = 0.2674 (from Excel NORMSDIST function). V = P[N(d 1 )] - t r RF Xe - [N(d 2 )] = $30(0.3700) - $35e (-0.05)(0.33333) (0.2674) = $11.1000 - $9.2043 = $1.8957 $1.90. 8-5 The stock’s range of payoffs in six months is $18 - $13 = $5. At expiration, the option will be worth $18 - $14 = $4 if the stock price is $18, and zero if the stock price $13. The range of payoffs for the stock option is $4 – 0 = $5.
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Unformatted text preview: Equalize the range to find the number of shares of stock: Option range / Stock range = $4/$5 = 0.8. With 0.8 shares, the stocks payoff will be either 0.8($18) = $14.40 or 0.8($13) = $10.40. The portfolios payoff will be $14.4 - $4 = $10.40, or $10.40 0 = $10.40. The present value of $10.40 at the daily compounded risk-free rate is: PV = $10.40 / (1+ (0.06/365)) 365/2 = $10.093. Mini Case: 8 - 1 The option price is the current value of the stock in the portfolio minus the PV of the payoff: V = 0.8($15) - $10.093 = $1.907 .$1.91. SOLUTION TO SPREADSHEET PROBLEMS 8-7 The detailed solution for the problem is available both on the instructors resource CD-ROM (in the file Solution for FM 11 Ch 08 P07 Build a Model.xls ) and on the instructors side of the textbooks web site, http://brigham.swcollege.com. Mini Case: 8 - 2...
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This note was uploaded on 04/12/2011 for the course ECON 101 taught by Professor Buddin during the Spring '08 term at UCLA.

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answers-odd-problems-ch08 - Equalize the range to find the...

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