17. The current price of United Carbon (UC) stock is $200. The standard deviation is 22.3% a year, and the interest rate is 21% a year. A one-year call option on UC has an exercise price of $180.

a. Use the Black–Scholes model to value the call option on UC. You may find it helpful to use the “live” spreadsheet in Table 21.2 on the book’s Web site, www.mhhe.com/

bma.

b. Use the formula given in Section 21-2 to calculate the up and down moves that you would use if you valued the UC option with the one-period binomial method. Now value the option by using that method.

c. Recalculate the up and down moves and revalue the option by using the two-period binomial method.

d. Use your answer to part

(c) to calculate the option delta (i) today; (ii) next period if the stock price rises; and (iii) next period if the stock price falls. Show at each point how you would replicate a call option with a levered investment in the company’s stock.