3. Today's price of stock X amounts to 60. The price in a year from now is predicted to be either 90 or 30. The risk free interest rate is 20%. . a) To which type of option does a stock option belong that al- lows you to buy the underlying asset at a strike price of 50 at maturity? b) Explain under which conditions such an option will not be ex- ercised. c) Set up a table that shows the state-contingent payoffs for the stock and for the option. d) Use the state contingent payoffs to set up two equations that allow you to derive the Levered Hedging Portfolio for the op- tion. Derive the amount of stocks and credit needed for the LHP. 3. Today's price of stock X amounts to 60. The price in a year from now is predicted to be either 90 or 30. The risk free interest rate is 20%. . a) To which type of option does a stock option belong that al- lows you to buy the underlying asset at a strike price of 50 at maturity? b) Explain under which conditions such an option will not be ex- ercised. c) Set up a table that shows the state-contingent payoffs for the stock and for the option. d) Use the state contingent payoffs to set up two equations that allow you to derive the Levered Hedging Portfolio for the op- tion. Derive the amount of stocks and credit needed for the LHP