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# 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 stock’s payoff will be either 0.8(\$18) = \$14.40 or 0.8(\$13) = \$10.40. The portfolio’s 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 instructor’s resource CD-ROM (in the file Solution for FM 11 Ch 08 P07 Build a Model.xls ) and on the instructor’s side of the textbook’s web site, http://brigham.swcollege.com. Mini Case: 8 - 2...
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answers-odd-problems-ch08 - Equalize the range to find the...

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