Week 2 Sol

Week 2 Sol - 8-1 Exercise value = Current stock price...

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8-1 Exercise value = Current stock price – strike price = $30 - $25 = $5. Time value = Option price – Exercise value = $7 - $5 = $2. 8-3 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 )] - [N(d 2 )] = $15(0.59675) - $15e (-0.06)(0.5) (0.50000) = $8.95128 - $15(0.9512)(0.50000) = $1.6729 $1.67. 8-4 Put = V – P + X exp(-r RF t) = $6.56 - $33 + $32 e -0.06(1) = $6.56 - $33 + $30.136 = $3.696 $3.70. 8-6 The stock’s range of payoffs in one year is $26 - $16 = $10. At expiration, the option will be worth $26 - $21 = $5 if the stock price is $26, and zero if the stock price $16. The range of payoffs for the stock option is $5 – 0 = $5. Equalize the range to find the number of shares of stock: Option range / Stock range = $5/$10 = 0.5. With 0.5 shares, the stock’s payoff will be either $13 or $8.
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Week 2 Sol - 8-1 Exercise value = Current stock price...

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