A certain mining company is listed on the Toronto Stock Exchange. We assume that the (discounted) price of a share of this company at time t is given by the random variable S_you, for t = 0, 1, 2, 3, . . .. Following econometric studies, it is estimated that the evolution of the price of this stock is adequately described by a binomial process such as

St = uSt1 with probability p = 0.6

dSt1 with probability q = 0.4

where u = 1.2 and d = 1/u, for t = 1, 2, 3, . . ., the share price currently being S₀= $100. An investor examines the possibility of building up a portfolio of stocks and options which would then be liquidated after three periods. Thus, at t = 0 he would buy a certain number of shares and options, then at t = 3 he would sell the shares and he would exercise his options if this was to his advantage. The purchase price of an option is c = $20 at the moment (t = 0) with a (discounted) strike price set at K = $90 at the expiration date (t = 3).

1. 1. Calculate the marginal distribution of price S₃of the stock on the expiration date.
2. 2. Calculate the expected return of stocks and options in this market.