A stock is currently worth 100 , and each year it goes up or down by 20%. The risk-free interest rate is r=10% per annum compounded annually (i.e. the accumulation factor for one year is =1.1 ). a) Using the principle of risk-neutrality find the price for a 3-year Asian average price call option with the strike K=100 and the payoff V(S(1),S(2),S(3))=(A3K)+, where A3=3S(1)+S(2)+S(3) (note that here the initial price is excluded from the calculation of the average price). b) Using the principle of risk-neutrality find the price of a 3-year lookback option with payoff given by V(S(0),,S(3))=max(S(0),S(1),S(2),S(3))min(S(0),S(1),S(2),S(3)). c) Using the principle of risk-neutrality find the price of a 3-year down-and-out barrier put option with strike K=105 and barrier H=70, i.e. of a financial derivative with the path-dependent payoff given below V=V(S(0),,S(3))=0,105S(3),0,ifS(3)105,ifS(3)70,ifS(3)