Question 1: Consider a stock with current price 8$ which can go up by 20% with...

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Question 1: Consider a stock with current price 8$ which can go up by 20% with probability 40% or down by 20% with probability 60%. The process representing the evolution of the stock is {Sn}n=1,2 for two periods where we can have S = So u, Sod, Suu = So u, etc. Is {S}n=1,2 a martingale with respect to the above probability Sq S = 2 and the filtration (Sn)n=1,2 it generates? Hint: calculate E(S|S0). Question 1: Consider a stock with current price 8$ which can go up by 20% with probability 40% or down by 20% with probability 60%. The process representing the evolution of the stock is {Sn}n=1,2 for two periods where we can have S = So u, Sod, Suu = So u, etc. Is {S}n=1,2 a martingale with respect to the above probability Sq S = 2 and the filtration (Sn)n=1,2 it generates? Hint: calculate E(S|S0).