Buffelhead’s stock price is $220 and could halve or double in each six-month period (equivalent to a standard deviation of 98 percent). A one-year call option on Buffelhead has an exercise price of $165. The interest rate is 21 percent a year.

(a) What is the value of the Buffelhead call?

(b) Now calculate the option delta for the second six months if (i) the stock price rises to $440 and (ii) the stock price falls to $110.

(c) How does the call option delta vary with the level of the stock price? Explain intuitively why.

(d) Suppose that in month 6 the Buffelhead stock price is $110. How at that point could you replicate an investment in the stock by a combination of call options and riskfree lending? Show that your strategy does indeed produce the same returns as those from an investment in the stock.