Q7. MQU is a company which has developed a software product called Officesmart. Officesmart is designed to build up a smart mobile office for an enterprise. Users can install Officesmart on their computers or smart phones. Officesmart has functions such as a text messaging, email, conference call application, group project and cloud storage for colleagues who are grouped according to their departments. Users can easily use Officesmart to submit leave or reimbursement request and managers can immediately receive the notifications and respond immediately. Officesmart also has a clocking system that allows companies to track absence or working overtime. The current price of one MQU share is $35.50 and over the next month the share price will either increase by 5% (if the software has a positive market impact) or decrease by 5% (if the software has a negative market impact). A European call option on an MQU share will expire at the end of one month. The strike price is $35.00. MQU shares will not pay any dividends during the next month. You can borrow money today for one month at a rate of j₁₂ = 6% p.a

(a) Suppose you estimate the probability of a positive market response (an increase in customer numbers) to be 50%. Use the contingent payments method to find the amount you would be willing to pay today (i.e., the option premium) for the call option. (5dp). Include in your answer a carefully labelled contingent cash flow diagram that illustrates your modelling approach.

(b) Consider the replicating portfolio (that is, the investment strategy which will give identical payoffs, at the end of one month, to the call option) that involves buying h shares in MQU today, and borrowing $B for one month. Illustrate this model in a carefully labelled contingent cash flow diagram. Find the values of h and B (5dp).

(c)What is the initial cost (net outlay) today of investing in the replicating portfolio? Round your answer to three decimal places.

(d) What is the fair price (or premium) for the call option? Why? Round your answer to three decimal places.