Bob is a budding investment banker in the pricing team. He proposes the following toy model for a single-period market that consists of a risk-free money account and the stock CBA. The time length of the period is A. Let So denote the price of a share of CBA at time 0. At the end of the period (time A), its price either goes up to $a = Sou or down to Sa = Sod. Let q denote the probability that the share price goes up under the risk-neutral probability measure Q. The risk-free interest rate is r. Let a = 4 1. (2 marks] Write down the risk-neutral probability distribution of SA, the share price at time A. Express the probability mass function in terms of u, d and q. 2. (3 marks] Show that q = (Hint: the discounted share price is a martingale under 0.1 3. [3 marks] Find Var(SA), the variance of the share price at time A? Express your answer in terms of a, u and d. 4. [3 marks] Let u = pov and d = 1 = e-ov Show that Var(Sa) – Sšo?A for small A. Hint: et 1+x if x is close to zero. The final result is obtained by dropping terms involving higher power of A]