1. (30%) An investment bank is offering a new financial instrument called a "happy call." The happy call has a payoff at the end of the year equal to max [0.5S1, S1 $10], where S1 is the unknown price of a stock at the end of the year. You al- ways get something with the happy call. The market price of the stock today is $11. There are two ordinary call options with strike prices of $10 and $20 being traded in the market. The market prices of these two calls today are $1.5 and $0.5, respectively.
2. (a) Illustrate graphically the value of a long position in the happy call at the end of the year.
3. (b) What would be the fair price of the happy call today?