You want to buy a stock that is currently selling for $60. You forecast that in one year, the stock's price will be either $98 or $20, with equal probabilities.
There is a one-year call option on the stock available with an exercise price of $80. You are able to borrow at a rate of 6.50%. You would like to hedge your stock position using the call option
a. What will be the call's value if the stock price is $98 in one year? What will be the call's value if the stock price is $20 in one year?
b. What is the hedge ratio you should use?
c. Assume that you can purchase fractional shares of stock How many shares of stock would you buy?