1. In this problem, you will learn different investment strategies using options. You will use K as the strike price and ST as the price of the underlying stock at the time of the option’s maturity T. For each cases, graph how the payoff (not net profit) at T depends on ST . That is, have the payoff of the investment strategy on the y-axis and ST on the x-axis value. For full credit, you need to plot the payoff of each of the components that make up the investment strategy, and then the combined total. (Refer to the Lecture Note where Protective Put was discussed and it should be clear what you are supposed to do.)
(a) Covered Call : Long in stock + short in call option
(b) Gut : Long position in a put option with strike price of K1 + long position in a call option with strike price of K2, where K1 < K2
(c) Bull Spread : Buying a call with K1, and sell a call with K2, where K1 < K2
(d) Collar : Long in stock + long in put with K1 + short in call with K2, where K1 < K2
2. What is the future value (at the end of year 3) of $300 deposited at the end of year 1, $400 deposited at the end of year 2, and $200 deposited at the end of year 3 into an account that earns 12% compounded quarterly?