Wogle is a company which has developed a self-driving car called Gamma. Gamma is a fully autonomous car and does not have a steering wheel, gas pedal or brake pedal. Gamma can can sense its surrounding environment and self-navigate without human control. It has a unique system which can analysis the live road situation and maintain a safe distance to other cars on the road. Wogle just released a detailed report about their road testing results for Gamma. You are thinking of buying a European call option on shares in Wogle.

The current price of one Wogle share is $103.28 and over the next month the share price will either increase to $110.76 (if the report has a positive market impact) or decrease to $96.87 (if the report has a negative market impact).

The European call option will expire at the end of one month. The strike price is $105.00. The share will not pay any dividends during the next month. You can borrow money today for one month at a rate of = 6% p.a.

a. Suppose you estimate the probability of a positive market response (an increase in customer numbers) to be 70%. 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. (Round your answer to five decimal places.) 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 Wogle today, and borrowing $B for one month. Illustrate this model in a carefully labelled contingent cash flow diagram. Findthe values of h and B (round your answers to five decimal places).

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

d. What is the fair price (or premium) for the call option, if the arbitrage-free pricing principle is applied? Why? (Round your answer to five decimal places.)