Question 1: Binomial model Buffelhead's stock price is $220 and could halve or double in each six- month period (equivalent to a standard deviation of 98%). A one-year call option on Buffel- head has an exercise price of $165. The interest rate is 21% 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 stockprice 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 intui- tively 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 risk-free lend- ing? Show that your strategy does indeed produce the same returns as those from an investment in the stock.
Question 2: Recalculate the value of the Buffelhead call option, assuming that the option is American and that at the end of the first six months the company pays a dividend of $25. (Thus the price at the end of the year is either double or half the ex-dividend price in month 6.) How would your answer change if the option were European?