Only looking for answer to #9.

#8 At t=0, the price of a certain stock is S(0)=$50. At t=1, the price is either S(1)=$80 or S(1)=$30. A certain option contract is worth $10 if the stock price is $80, and is worth $0 if the stock price is $30. Assuming no arbitrage opportunities, and continuously compounded interest of 5%, what is the price of the option at time t=0?

#9 Suppose we are in the situation of problem 8, but a certain bank thinks that the option should be worth $5 for some reason and they are willing to sell you options at $5.1 and buy options from you at $4.9. Choose a portfolio of x shares of the stock and y options that you buy or sell at time 0 that will guarantee you a net return of $10^6 dollars at time 1.