Suppose the price of a company A’s stock is currently $100. Now let us assume that from one period to the next, the stock can go up by 17.5% or go down by 15%. In addition, let us assume that there is a 50% chance that the stock will go up and a 50% chance that a stock will go down. It is also assumed that the price movement of each a stock (or of the stock market) today is completely independent of its movement in the past; in other words, the price will rise or fall today by a random amount. In addition, suppose a call option has 3 periods to expiration. The underlying asset is stock A, the exercise price is $110, and the risk-free rate is 16%.
Lay out the paths that the stock’s price may take.
Determine the value of call option at the end of each period.
Determine the value of call option at time zero.
Calculate the hedge ratios for each period.
Construct an example showing how the hedge works. Make sure the example illustrates how the hedge portfolio earns the risk free rate over both periods.