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.
2. Recalculate the value of the Buffelhead call option (see Problem 12), 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?