Let r be the risk-free rate of one period. In the binomial model, the market movement is represented by the up factor u and the down factor d where d...

Let r be the risk-free rate of one period. In the binomial model, the market movement is represented by the up factor u and the down factor d where d < 1 + r < u. (i) Under the one-period binomial model, express the stock price Su after one up movement and the stock price Sd after one down movement in terms of u, d and the initial stock price S. (ii) Find the probabilities (q, 1 − q) such that S = 1 1 + r (qSu + (1 − q)Sd).