Question: Except where otherwise specified, all interest rates are stated as annual rates.
a. Obtain weekly prices for a stock of your choice for the 5-year period March 1, 2007 through March 1, 2017. The stock must have traded continuously for the entire 5-year period. (Use the adjusted closing prices from the "historical price" section for the stock from yahoo finance.) The prices must be submitted as part of the exam answers. Assuming the risk free interest rate is between 0.6875% and 1.3125% (but not 1%).
b. Calculate continuously compounded returns on the stock for each week during the last five years.
c. Determine the average weekly return on the stock.
d. Determine the standard deviation of weekly stock returns.
e. Calculate the average annual return and annual standard deviation for the stock.
f. Using the answers to e and assuming each period during of the year has length .00001 (that is, there are 100,000 sub-periods during the year), 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.
g. Select as a strike price an even dollar amount approximately 5% higher than the stock's current market price and determine how many upward stock price movements must occur in the next 9 months in order for a call option to be in the money.
h. Solve for p and p* for a call option on this stock.
i. Use the general binomial model (without constructing a lattice) to determine the price of a 9-month call option for this stock with the strike price selected in part g.