The current price of United Carbon (UC) stock is $200. The standard deviation is 22.3 percent a year, and the interest rate is 21 percent 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.

(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.