Based on historical data, the mean of the stock price at time t + T for small T > 0 is E[S(t + T)] = S(t)(1 + T) for some > 0.

The variance of S(t + T) is given by Var[S(t + T)] = S²(t)²T where ² > 0 is the annual variance.

Use mean and variance matching to build a BLM for the stock in the following case: u = 1 /d. Obtain expressions for u, d, p in terms of , , T