1. Select a stock that has traded continuously for the last 5 years. Obtain monthly prices for a stock for the 5-year period April 1, 2012 through April 1, 2017. (Use the “adj closing price” from the “historical price” section in yahoo finance as the stock price.)
2. Calculate continuously compounded return on the stock for each week during the last five years.
3. Determine the average monthly and average annual return on the stock.
4. Determine the standard deviation of monthly returns on the stock and the standard deviation of annual returns on the stock.
5. Using the answers to 4 and 5 and assuming each sub-period has length .0001 (that is, h=.0001), find a “u” and “d” that can be used in a binary model to estimate the periodic upward and downward movement of the stock price.
6. Select as a strike price that is an even dollar amount between 5% and 10% higher than the stock’s current market price.
7. Determine how many upward stock price movements must occur in the next 2500 periods in order for a call option to be in the money (that is, what is smallest “a” that satisfies the equation: uad(2500-a)S ³ K).
8. Assuming the annual risk free interest rate is 2.0% (this is the annual rate, you will need to determine the rate of sub-period h), solve for p and p* for an option on this stock.
9. Use the binomial model (without constructing a lattice) to determine the price of a 3-month (2500 period) call option for this stock with the strike price selected in number 6.