ABCis currently selling for $1800. At the end of three months, the price will either go up or down by 20%. Three months beyond that (i.e. six months from now), the volatility is expected to be lower. You now expect the price to have changed by 10% beyond the three-month price. Your client wants to buy a six-month American call option from you at a strike price of $1800. What do you charge him for the option if the risk-free rate is 5% per year? How do you hedge your risk by constructing a dynamic trading strategy? Give details of the exact number of shares you need to trade and amount of borrowing necessary at each stage.