You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1.2 million. Over the past five years, the price of land in the area has increased 10 percent per year, with an annual standard deviation of 19 percent. A buyer has recently approached you and wants an option to buy the land in the next 9 months for $1,310,000. The risk-free rate of interest is 7 percent per year, compounded continuously. How much should you charge for the option? (Round your answer to the nearest $1,000.)
d1 = [ln ($1,200,000/$1,310,000) + (0.07 + 0.192/2) × (0.75)]/[0.19 × (0.751/2)] = -0.13168497
d2 = -0.077157 - [0.19 × (0.751/2)] = -0.2962298 N(d1) = 0.4476 N(d2) = 0.3835 C = $1,200,000(0.4476) - ($1,310,000e-0.07(0.75)) (0.3835) = $60,415.96 ≈ $60,000 |
77.
| A call option with an exercise price of $31 and 6 months to expiration has a price of $3.77. The stock is currently priced at $17.99, and the risk-free rate is 3 percent per year, compounded continuously. What is the price of a put option with the same exercise price and expiration date?
$17.99 + P = $31e-0.03(0.5) + $3.77; P = $16.32
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78.
| A call option matures in nine months. The underlying stock price is $90, and the stock's return has a standard deviation of 19 percent per year. The risk-free rate is 3 percent per year, compounded continuously. The exercise price is $0. What is the price of the call option?
If the exercise price is equal to zero, the call price will equal the stock price, which is $90.
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79.
| A stock is currently priced at $45. A call option with an expiration of one year has an exercise price of $60. The risk-free rate is 14 percent per year, compounded continuously, and the standard deviation of the stock's return is infinitely large. What is the price of the call option?
If the standard deviation is infinite, d1 goes to positive infinity so N(d1) goes to 1, and d2 goes to negative infinity so N(d2) goes to 0. In this case, the call price is equal to the stock price, which is $45.
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